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Simulia-UK2013-CONTACT_SEMINAR.pdf
Ι www.3ds.com Ι © Dassault Systèmes Ι Confidential Information Ι 18/03/2013 ref.: 20100928MKT038 Ι
Solving Contact Problems with Abaqus
DS UK Ltd, Coventry - March 2013
Stephen King
Tony Richards
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Seminar Abstract
Contact interactions between different parts play a key role when simulating
bolted assemblies, manufacturing processes, dynamic impact events, and
various other systems. Accurately capturing these interactions is essential for
solving many engineering problems. SIMULIA has developed state-of-the-art
contact modeling capabilities in Abaqus.
Attend this seminar to learn the latest techniques and strategies for solving
difficult contact problems with Abaqus. This seminar primarily focuses on
Abaqus/Standard, with additional discussion of Abaqus/Explicit.
Topics include advantages of the general contact capability, accurate contact
pressures, insight on numerical methods, tips for improving convergence,
recent enhancements to the implicit dynamics procedure for contact models,
and proper representation of physical details associated with contact.
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Lectures
• Lecture 1:
Introduction
• Lecture 2:
Defining Contact in an Analysis
• Lecture 3:
Numerical Methods for Contact
• Lecture 4:
Contact Output and Diagnostics Tools (start)
(Lunch) 12:30pm – 1.30pm
• Lecture 4 (cont.): Contact Output and Diagnostics Tools (finish)
• Lecture 5:
Convergence Topics
• Lecture 6:
Contact in Abaqus/Explicit
• Lecture 7:
More Features
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Legal Notices
All Dassault Systèmes Software products described in this documentation are available only
under license from Dassault Systèmes or its subsidiary/subsidiaries and may be used or
reproduced only in accordance with the terms of such license.
The information in this document is subject to change without prior notice. Dassault Systèmes
and its subsidiaries shall not be responsible for the consequences of any errors or omissions
that may appear in this documentation.
No part of this documentation may be reproduced or distributed in any form without prior
written permission of Dassault Systèmes or its subsidiary/subsidiaries.
© Dassault Systèmes, 2013.
Printed in the U. S. A.
The 3DS logo, SIMULIA, CATIA, 3DVIA, DELMIA, ENOVIA, SolidWorks, Abaqus, Isight, and
Unified FEA are trademarks or registered trademarks of Dassault Systèmes or its subsidiaries
in the US and/or other countries. Other company, product, and service names may be
trademarks or service marks of their respective owners.
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Introduction
Lecture 1
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Overview
• General Considerations
• Evolution of Contact in Abaqus
• Contact Examples
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General Considerations
• What is contact?
• Physically, contact involves interactions between bodies
• Contact pressure resists penetration
Fairly
intuitive
• Frictional stress resists sliding
• Electrical, thermal interactions
• Numerically, contact includes severe nonlinearities
Numerically
challenging
• Inequality conditions result in discontinuous
―stiffness‖
• Gap distance: dgap ≥ 0
• Frictional stress: t ≤ mp
• Conductance properties suddenly change
when contact is established
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General Considerations
• Various classifications of contact interactions can be considered
• Example: slender or bulky components
• Bulky components:
• Typically many nodes in contact
at one time
• Contact causes local deformation
and shear, but it causes little bending
• Slender components
• Often relatively few nodes in contact at
one time
• Contact causes bending
• Often more challenging
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General Considerations
• Classifications of contact
interactions:
• Slender or bulky components
• Deformable or rigid surfaces
• Degree of confinement and
compressibility of components
• Two-body contact or selfcontact
• Amount of relative motion
(small or finite sliding)
• Amount of deformation
• Underlying element type (1st or
2nd order)
• Interaction properties (friction,
thermal, etc.)
• Which results are of interest
and importance (e.g. contact
stresses)
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„Ingredients‟ of a Contact Model
• Contact surfaces
• Surfaces over bodies that may experience contact
• Contact interactions
• Which surfaces interact with one another?
• Surface property assignments
• For example, contact thickness of a shell
• Contact property models
• Examples: pressure vs. overclosure relationship, friction coefficient, conduction
coefficients, etc.
• Contact formulation aspects
• For example, can a small-sliding formulation be used?
• Algorithmic contact controls
• Such as contact stabilization settings
Many of these aspect need not be
explicitly specified
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General Considerations
• Physical and numerical aspects of contact modeling:
• User responsible for defining physical aspects of model
• User and Abaqus control various numerical aspects
• Many details (e.g., slender or bulky classification) need not be
explicitly specified
• Trend toward greater automation
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Evolution of Contact Modeling in
Abaqus
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Evolution of Contact Modeling
Contact elements
(e.g., GAPUNI):
Contact pairs:
General contact:
2
n
v
h
1


h  d  n  u2  u1  0
User-defined element for
each contact constraint
Many pairings
for assemblies
Trends over time
Model all interactions
between free surfaces
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Evolution of Contact Modeling
Flat approximation of master
surface per slave node:
Master surface
Realistic representation of
master surface:
Master surface
Trends over time
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Evolution of Contact Modeling
Slave surface treated as
collection of discrete points:
Constraints based on
integrals over slave surface:
Does not resist
penetration at
master nodes
Resists penetration
at slave nodes
Good resolution of
contact over the
entire interface
Trends over time
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Evolution of Contact Modeling
• Goals: improve usability, accuracy, and performance
• More focus by user on physical aspects
• Less on idiosyncrasies of numerical algorithms
• Broad applicability
• Large models (assemblies)
General contact:
Constraints based on
integrals over slave
surface:
Realistic representation of
master surface:
Master surface
Good resolution of
contact over the
entire interface
Model all interactions
between free surfaces
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Evolution of Contact Modeling
• General contact algorithm
• Contact domain spans multiple bodies
(both rigid and deformable)
• Default domain defined automatically
via all-inclusive, element-based surface
• Method geared toward models with multiple
components and complex topology
• Greater ease in defining contact model
• Available in Abaqus/Explicit since 6.3
• Available in Abaqus/Standard since 6.8-EF
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Evolution of Contact Modeling
• Transition to general contact nearly complete for Abaqus/Explicit
• Most Abaqus/Explicit analyses use general contact
• Easy to use and robust
• Accuracy, performance, and scalability as good or better than contact pairs
• Some features available only in general contact
• A few features available only with contact pairs
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Evolution of Contact Modeling
• Transitioning to general contact in Abaqus/Standard
• Good feedback
• Easier to create model than contact pairs
• Similar robustness and accuracy as contact pairs
• Some extra contact tracking time, etc.
• Contact pairs are required to access specific features not yet available
with general contact
• Analytical rigid surfaces
• Node-based surfaces or surfaces on 3-D beams
• Small-sliding formulation
• See the Abaqus Analysis User’s Manual
• General contact and contact pairs can be used together
• General contact algorithm automatically avoids processing interactions
treated with contact pairs
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Contact Examples
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Contact Examples
• Contact between linear elastic bodies with small relative motion
• Common design problems involving:
• Small relative motion
• Significant contact area
• Typical examples:
• Bearing design
• Hard gaskets
• Interference fits
• Fretting (surface wear) is
often a concern, requiring
accurate resolution of contact
stresses and stick/slip zones
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Contact Examples
• Deformable-to-rigid contact
• Finite sliding between
surfaces (large
displacements)
• Finite strain of deforming
components
• Typical examples:
• Rubber seals
• Tire on road
• Pipeline on seabed
• Forming simulations
(rigid die/mold,
deformable
component)
Example: metal forming simulation
Example taken from ―Superplastic forming of
a rectangular box,‖ Section 1.3.2 in the
Abaqus Example Problems Manual
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Contact Examples
• Finite-sliding contact between
deformable bodies
• Most general category of
contact
• Example: twisting blocks
• Press together and
relative rotation of 90°
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Contact Examples
• Self-contact
• Type of finite-sliding,
deformable-to-deformable
contact
SURF1
(rigid)
SURF2
• Contact of a single body with
itself—often involves severe
deformation
• Sometimes adds CPU
expense and numerical difficulty
• General contact implementation
somewhat like self-contact of
surface spanning multiple
bodies
Contour of minimum principal stress
Example: compression of a rubber gasket
Example taken from ―Self-contact in
rubber/foam components: rubber gasket,‖
Example Problem 1.1.18 in the Abaqus
Example Problems Manual
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Lecture 1 Summary
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Review of Topics Discussed in Lecture
• General Considerations
• Evolution of Contact in Abaqus
• Contact Examples
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Defining Contact
Lecture 2
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Overview
• Defining Surfaces
• Defining Contact Pairs
• Defining General Contact
• Representation of Curved Surfaces
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Defining Surfaces
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Surfaces
• Various Abaqus features use surfaces
• Contact
• Tie constraints
• Surface loads
• Cavity radiation
• Bolt pre-tensioning
• Various surface types exist in Abaqus
• Element-based (most common)
• Node-based
• Analytical rigid
• Eulerian (not covering coupled Eulerian-Lagrangian analysis in this seminar)
• Surface documentation
• Sections 2.3.1–2.3.6 of Abaqus Analysis User’s Manual
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Surfaces
• Abaqus/CAE interface
Solid bodies
• Surface on solid defined
by selecting appropriate region
of exterior of the part
• Regions can be selected individually
or based on face angles
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Surfaces
• Abaqus/CAE interface
Shell-like surfaces may be:
• On ―positive‖ side of elements
• On ―negative‖ side of elements
• Or, on both sides
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Surfaces
• Element-based surfaces are composed of element faces
• Typically, on exposed faces of bodies
Close-up view
with local face
ID labels
Local numbering conventions
for brick and tet elements
Example of surface
defined over a
portion of rivet
• Characteristics inherited from underlying elements include:
• Deformable or rigid
• Shell/membrane thickness
• Some contact formulations account for this thickness
• Representative stiffness
• Influences some numerical aspects, such as penalty stiffness
Surface Restrictions
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• Mostly context-specific
• Depend on which features use the surface
• Restrictions on surfaces used in contact definitions
• Depend on details of contact definition
• Documented in Abaqus Analysis User’s Manual
• Trend toward fewer surface restrictions
Connected
at one node
• Example: master surface connectivity requirements
Discontinuous
T-intersection
(or 3-D faces joined
at only one node)
(more than two
faces per edge)
Finite-sliding,
node-to-surface
Not allowed
Not allowed
Finite-sliding,
surface-to-surface
Allowed
Allowed
Contact
formulation
T-intersection
• Example of a general restriction on element-based surfaces
• Parent elements cannot be a mixture of two-dimensional,
axisymmetric, and three-dimensional elements
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Defining Contact Pairs
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Defining Contact Pairs
• Features of contact pairs defined by user:
• What constitutes each surface
• Which pairs of surfaces will interact
• Which surface is the master and which is the slave
• Which surface interaction properties are relevant
(e.g., friction)
Potential for
many pairings
Defining Contact Pairs
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axis of symmetry
• Example: analysis of a jounce bumper
• Highly compressible component used in a
vehicle’s shock isolation system
• Bumper folds as it is compressed, so selfcontact is modeled
Final
deformed
shape
• Analysis consists of two steps:
Step 1 Resolve interference fit
Step 2 Move the bottom plate up to
compress the bumper
top
plate
shaft
bumper
bottom
plate
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Defining Contact Pairs
TOPPLATE
1• Define surfaces (using Abaqus/CAE)
Double-click Surfaces to
create a new surface
SHAFT
BUMPER-EXT
Model Tree
BOTPLATE
Create discrete rigid part
Defining Contact Pairs
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Surface
TOPPLATE
1• Define surfaces (using keywords)
• Automatic free surface generation on bumper
elements:
*SURFACE,NAME=BUMPER-EXT
BUMPER,
Surface
SHAFT
• Discrete rigid surfaces:
*RIGID BODY, ELSET=BOTDIE, REF NODE=BOTRP
*SURFACE,NAME=BOTPLATE
BOTDIE, SPOS
*RIGID BODY, ELSET=TOPDIE, REF NODE=TOPRP
*SURFACE, NAME=TOPPLATE
TOPDIE, SPOS
Element
set
BUMPER
Surface
BUMPER-EXT
*RIGID BODY, ELSET=SHAFTDIE, REF NODE=SHAFTRP
*SURFACE, NAME=SHAFT
SHAFTDIE, SPOS
Surface
BOTPLATE
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Defining Contact Pairs
2• Define contact properties
• Contact property definitions are the same
for general contact and contact pairs
• Contact properties can include:
• Friction
• Contact damping
• Pressure-overclosure relationships
• All contact pairs use the same interaction
property in this example:
*SURFACE INTERACTION, NAME=Friction
*FRICTION
0.05,
Defining Contact Pairs
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TOPPLATE
3• Define contact pairs
• Contact pair definition required for
each pair of surfaces that can interact
SHAFT
• Bumper self-contact:
include inside
step definition
*CONTACT PAIR, INTERACTION=Friction
BUMPER-EXT,
BUMPER-EXT
BOTPLATE
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Defining Contact Pairs
TOPPLATE
3• Define contact pairs
• Contact between the bumper and
the rigid bodies:
SHAFT
*CONTACT PAIR, INTERACTION=Friction
BUMPER-EXT, TOPPLATE
BUMPER-EXT, BOTPLATE
BUMPER-EXT, SHAFT
BUMPER-EXT
BOTPLATE
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Defining Contact Pairs
• Automatic contact pair detection in Abaqus/CAE
• Automatic contact detection is a fast and easy way to define contact
pairs and tie constraints in a three-dimensional model
• Instead of individually selecting surfaces and defining the interactions
between them, you can instruct Abaqus/CAE to locate automatically all
surfaces in a model that are likely to interact based on initial proximity
• Can be used to define contact with shells, membranes, and solids
• Including shell offset
• Native or orphan mesh parts
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Defining Contact Pairs
• Automatic contact pair detection in Abaqus/CAE
• Example: Disk brake
• Tabular display of candidate contact pairs is provided
• Various controls over selection criteria, etc.
Shortcuts; e.g.,
manually add contact
pairs to the group
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Defining General Contact
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Defining General Contact
• General contact user interface allows for
concise contact definition reflecting the
physical description of the problem
Typical usage of
general contact:
• Contact definition can be expanded in
complexity, as needed
• Independent specification of contact
interaction domain, contact properties,
and surface attributes permitted
• Minimal algorithmic controls required
• General contact user interface is very
similar for Abaqus/Explicit and
Abaqus/Standard analyses
Model all interactions
between free surfaces
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Defining General Contact
• Examples of differences between general contact in Abaqus/Explicit
and Abaqus/Standard
Characteristic
Abaqus/Explicit
Abaqus/Standard
Primary formulation
Node-to-surface
Surface-to-surface
Master-slave roles
Balanced master-slave
Pure master-slave
Secondary formulation
Edge-to-edge
Edge-to-surface
2-D and axisymmetric
Not available
Available
Most aspects of
contact definition
Step-dependent
Model data
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Defining General Contact
• Jounce bumper example using general
contact
axis of symmetry
• Recall initial and final configurations
(shown here)
top
plate
shaft
bumper
bottom
plate
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Defining General Contact
• Contact definition
1) Begin the general contact definition
*Contact
*Contact Inclusions, ALL EXTERIOR
2) Specify ―automatic‖ contact
for the entire model
3) Assign global contact properties
*Contact Property Assignment
,
, FRICTION
Simple!
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Defining General Contact
• The contact definition can gradually become more detailed, as called
for by the analysis
• Global/local friction coefficients and other contact properties can be
defined
• Pair-wise specification of contact domain (instead of ALL EXTERIOR)
allowed
• Contact inclusions and contact exclusions
• User control of contact thickness (especially for shells) is provided
• Surface properties
• Contact initialization (initial adjustments, interference fits, etc.)
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Defining General Contact
Surface
• Fine-tuning contact domain
TOPPLATE
• General contact domain can be modified by
including and/or excluding predefined surfaces
• For example, exclude consideration of contact
between rigid surfaces in this example
Surface
SHAFT
• Not essential for this analysis (overlap between
perpendicular surfaces not resolved with the
surface-to-surface contact formulation used by
general contact)
Surface
BUMPER-EXT
Surface
BOTPLATE
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Defining General Contact
Surface
• Keyword interface for contact exclusions:
TOPPLATE
Surface
SHAFT
*Contact
*Contact Inclusions, ALL EXTERIOR
*Contact Exclusions
TOPPLATE , SHAFT
No effect on results
TOPPLATE , BOTPLATE
of this analysis
SHAFT , BOTPLATE
*Contact Property Assignment
, , FRICTION
Surface
BUMPER-EXT
Surface
BOTPLATE
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Defining General Contact
• Contact initialization
• The default behavior of general contact is to adjust
small initial overclosures without strain
• Can instead treat as interference fits
Surface
SHAFT
Surface
BUMPER-EXT
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Defining General Contact
• Contact initialization
• Keyword interface:
Surface
SHAFT
*Contact Initialization Data,
name=Fit-1, INTERFERENCE FIT
*Contact
*Contact Inclusions, ALL EXTERIOR
*Contact Property Assignment
, , FRICTION
*Contact Initialization Assignment
BUMPER-EXT, SHAFT, Fit-1
Surface
BUMPER-EXT
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Defining General Contact
• Contact properties
• Pertains to aspects such as:
• Contact pressure-overclosure relationship
• Friction
• Contact damping
• Defaults:
• A ―hard‖ pressure-overclosure relationship
• No contact pressure until nodes are in contact
• Unlimited contact pressure once contact has been established
(enforced with a penalty method)
• No friction
• No contact damping
• User can override contact property defaults globally and locally
• Last assignment applies in case of conflicting assignments
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Defining General Contact
• Example: Bolted flange
• Coefficient of friction m = 0.1 for all
contact interactions except for those
involving the gasket (m = 0.4)
*Contact Property Assignment
,
, Friction-0p1
, gasketAll, Friction-0p4
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Representation of Curved Surfaces
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Representation of Curved Surfaces
• Having faceted representations of curved surfaces is sometimes
detrimental to accuracy and convergence
• Geometry corrections for the surfaceto-surface contact formulation improve
these aspects without degrading the
per-iteration performance
• Available for near-axisymmetric
and near-spherical surfaces
• Example applications on
subsequent slides
Master
surface
Slave
surface
Correction
factors
• Whereas, surface-smoothing options for the node-to-surface contact
formulation primarily target convergence issues associated with having
discontinuous surface normals
• But generally do not strive to represent exact initial geometry
• Details depend on whether surfaces are 2-D or 3-D, rigid or
deformable (not discussed in this seminar)
Will discuss contact formulations in next lecture
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Representation of Curved Surfaces
• Effect of geometric corrections in a piston application
Rod and piston-to-pinion
Piston-to-cylinder
Cap and rod-to-crank
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Representation of Curved Surfaces
• Example: Concentric rings with interference fit and finite sliding
• Spin inner ring after resolving interference (frictionless)
• Analytical solution: Uniform pressure stress per ring
Noisy solution with
faceted geometry
Accurate solution with
geometric corrections
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Representation of Curved Surfaces
• Applicability of geometric corrections:
• Significant effect for small-to-moderate deformation
• Effect usually insignificant after large deformation
• Small- or finite-sliding, surface-to-surface contact formulation
• Applicable to the most-common curved
geometries; portions of surface geometry
must be approximately:
Axisymmetric
• Circular in 2-D
• Axisymmetric or spherical in 3-D
Spherical
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Representation of Curved Surfaces
• Abaqus/CAE automatically detects these surfaces in native geometry
models and applies appropriate smoothing method in contact interactions
General contact
Contact pairs
• Benefits:
• Improved accuracy
• Avoid need for matched nodes across contact interface
• Reduced iteration count (sometimes)
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Representation of Curved Surfaces
• Keyword interface for general contact
*Contact
*Contact Inclusions, All Exterior
*Surface Property Assignment, Property=Geometric Correction
surface_name, CIRCUMFERENTIAL, Xa, Ya
2-D: Center of circle
surface_name, CIRCUMFERENTIAL, Xa, Ya, Za, Xb, Yb, Zb
surface_name, SPHERICAL, Xa, Ya, Za
3-D: Center of sphere
y
*Contact
*Contact Inclusions, All Exterior
*Surface Property Assignment, Prop=Geom
Surf_1, CIRCUMFERENTIAL, 1.5, 0.0
Surf_2a, CIRCUMFERENTIAL, -2.5, 0.0
Surf_2b, CIRCUMFERENTIAL, 2.5, 0.0
Surf_1
x
Surf_2
Semi-circle on the
left side of Surf_2
Semi-circle on the
right side of Surf_2
3-D: 2 points on
symmetry axis
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Representation of Curved Surfaces
• Keyword interface for surface-to-surface contact pairs
*Contact Pair, Type=Surface to Surface, Geometric
Correction=smoothing_name
*Surface Smoothing, Name=smoothing_name
2-D: Center of circle
slave_region, master_region, CIRCUMFERENTIAL, Xa, Ya
slave_region, master_region, CIRCUMFERENTIAL, Xa, Ya, Za, Xb, Yb, Zb
3-D: 2 points on
slave_region, master_region, SPHERICAL, Xa, Ya, Za
symmetry axis
3-D: Center of sphere
y
*Contact Pair, Type=Surface, Geom=Smooth1
Surf_1, Surf_2
*Surface smoothing, Name=Smooth1
Surf_1, , CIRCUMFERENTIAL, 1.5, 0.0
, Surf_2a, CIRCUMFERENTIAL, -2.5, 0.0
, Surf_2b, CIRCUMFERENTIAL, 2.5, 0.0
Surf_1
x
Surf_2
Semi-circle on the
left side of Surf_2
Semi-circle on the
right side of Surf_2
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Representation of Curved Surfaces
• Example: Conical contact interface
Without any surface
geometry correction
With circumferential
smoothing
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Representation of Curved Surfaces
• Example: Spherical contact interface
• Uniform interference fit
Without any surface
geometry correction
With spherical
smoothing
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Representation of Curved Surfaces
• Capability applicable even if surface geometry deviates somewhat from perfect
cylinder, sphere, etc.
• Example: Interference fit between elliptical disk and circular ring
Undeformed
Deformed
Without any surface
geometry correction
With circumferential
correction
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Representation of Curved Surfaces
• Clamp example
Slave surfaces
of contact pairs
Hollow
tubes
General contact
internal surface
1000
Analysis time
(sec)
750
STD
PRE
500
250
0
CP
#
iterations
36
GC
GC
faceted smooth
55
41
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Representation of Curved Surfaces
• Clamp example (cont.)
• Contact pair model does not
consider contact involving shank
• Coarse refinement near bolt holes
New
output in
Abaqus
6.9-EF
• Nonphysical initial overclosures for
general contact without circumferential
smoothing
• Realistic small gaps at these interfaces
for general contact with circumferential
corrections activated
• Shank remains cylindrical
•
•
D=5
Slave surfaces of
contact pairs
More realistic
―STRAINFREE‖ output is 0.0
• Improved performance
Shank cross-section adjusted
to conform to hole facets
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Lecture 2 Summary
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Review of Topics Discussed in this Lecture
• Defining Contact Pairs
• Defining Surfaces for Contact Pairs
• Defining General Contact
• Representation of Curved Surfaces
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Numerical Methods
Lecture 3
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Overview
• Contact Formulation Aspects
• Contact Discretization
• Contact Enforcement
• Incrementation and Newton Iterations
• Summary
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Contact Formulation Aspects
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Contact Formulation Aspects
• Discretization
• How are constraints formed?
• For example, how to calculate gap or penetration
distances from nodal positions
• Node-to-surface, surface-to-surface, and
edge-to-surface formulations
• Enforcement
• How are constraints enforced?
• For example, numerical method to resist
penetrations
• Direct (Lagrange multipliers) or penalty
• Evolution of discretization
• How do constraints evolve upon sliding?
• Rigorous, nonlinear evolution (―finite sliding‖) vs.
approximate (―small sliding‖)
Contact formulation
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Contact Discretization
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Contact Discretization
• Node-to-surface technique
• Nodes on one surface (the slave surface) contact the
segments on the other surface (the master surface)
• Contact enforced at discrete points (slave nodes)
• Surface-to-surface technique
• Contact enforced in an average sense over a region
surrounding each slave node
• Slave surface much more than just a collection of nodes
• Fundamental to the development of general contact in
Abaqus/Standard
• Edge-to-surface technique
• Contact between a feature edge and a surface
• Enforced in an average sense over portions of feature
edges
• Supplemental formulation for general contact starting in
Abaqus/Standard 6.11
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Contact Discretization
• Node-to-surface (N-to-S) contact discretization
• Traditional ―point-against-surface‖ method
• Each potential contact constraint with this formulation
involves a ―slave‖ node and a ―master‖ facet
Slave surface
Master surface
This node of the master surface does not
participate in any contact constraints
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Contact Discretization
• Key implications of node-to-surface
formulation
Master
• Slave nodes cannot penetrate master
surface facets
• Master nodes are not explicitly restricted
from penetrating slave surface facets (and
sometimes do penetrate the slave surface)
Slave
• Refinement of slave surface helps avoid
gross penetration of master nodes into
slave surface
• Guidelines for master and slave roles
• More-refined surface should act as slave
surface
Slave
• Stiffer body should be master
• Active contact region should change most
rapidly on master surface
• Minimizes contact status changes
Master
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Contact Discretization
• While refinement of slave surface leads to global accuracy, local contact stress
oscillations may still be observed with N-to-S
Uniform pressure load, s =100
• 13% noise in CPRESS solution with N-to-S contact
discretization if top block acts as slave (shown above)
• 31% CPRESS noise if bottom block acts as slave (not shown)
• 2-D example
Ideal contact force distribution factors
(uniform pressure, linear elements):
1/6
1/4
1/3
1/3
1/2
1/6
1/4
11% deviation
Factors on master nodes assuming
ideal factors on slave nodes:
1/6
1/3
1/3
1/6×1 + ⅓×⅓ 2×⅓×⅔
= 5/18
= 8/18
1/6 Slave
Master
5/18
• ―Matching meshes‖ across contact interface avoids this noise
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Contact Discretization
• Surface-to-surface (S-to-S) contact discretization
• Each contact constraint is formulated based on an integral over the
region surrounding a slave node
slave
master
• Tends to involve more master
nodes per constraint
• Especially if master surface is
more refined than slave surface
• Also involves coupling
among slave nodes
• Still best to have the more-refined surface act as slave
• Better performance and accuracy
• Benefits of surface-to-surface approach
• Reduced likelihood of large localized penetrations
• Reduced sensitivity of results to master and slave roles
• More accurate contact stresses (without ―matching meshes‖)
• Inherent smoothing (better convergence)
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Contact Discretization
• S-to-S discretization often improves
accuracy of contact stresses
• Related to better distribution of
contact forces among master nodes
• Example: Classical Hertz contact
problem:
• Contact pressure contours much
smoother and peak contact
stress in very close agreement
with the analytical solution using
surface-to-surface approach
Analytical CPRESSmax = 3.01e+05
CPRESSmax =
3.425e+05
Node-to-surface
CPRESSmax =
3.008e+05
Surface-to-surface
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Contact Discretization
• S-to-S discretization reduces likelihood of snagging
Node-to-surface
Surface-to-surface
slave
slave
master
master
Treating slave surface as collection of
points can trigger snagging as slave
nodes traverse a corner
Computing average penetrations and slips
over finite regions has smoothing effect
that avoids snagging
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Contact Discretization
• S-to-S discretization reduces likelihood of master nodes
penetrating slave surface
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Contact Discretization
• S-to-S discretization reduces likelihood of master nodes
penetrating slave surface (another example)
master surface
constrained region
slave surface
Node-to-surface
results
Surface-to-surface
results
Non-ideal slave
and master
roles
Some penetration
may be observed
at individual nodes;
however, large,
undetected
penetrations of
master nodes into
slave surface do
not occur
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Contact Discretization
• S-to-S discretization much less sensitive to choice of master and slave
surfaces
• Results with S-to-S discretization nearly independent of master/slave
roles in this example:
Master
Slave
Slave
Master
Choosing slave surface to be finer mesh will still yield better results; choosing the
master surface to be more refined surface will tend to increase analysis cost
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Contact Discretization
• S-to-S discretization will generate multiple constraints at corners when
appropriate
Node-to-surface
• Single constraint in ―average‖
normal direction at corner
• Not stable
• Leads to large penetrations
and snagging
• Workaround: Two contact pairs
Surface-to-surface
• Two constraints are generated at
corner (even if one contact pair)
• See arrows near corner
• Accurate and stable
• No smoothing of surface normals
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Contact Discretization
• S-to-S discretization takes into consideration shell and membrane
thicknesses when performing contact calculations
• N-to-S considers this effect only for the small-sliding formulation
Thickness taken
into account
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Contact Discretization
• S-to-S discretization is fundamentally sound for situations in which quadratic
elements underlie slave surface
• N-to-S struggles with some quadratic element types
• Related to:
• Discrete treatment of slave surface
• ―Consistent‖ force distribution for element
• Workarounds (with pros and cons):
• C3D10M, supplementary constraints, etc.
q
q
q
q
1
pA
3
Zero force at
corner nodes
Uniaxial pressure loading of 5.0
Slave:
C3D10
Master:
C3D8
Node-to-surface
Surface-to-surface
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Contact Discretization
• S-to-S discretization has greater tendency to generate unsymmetric
stiffness terms where master and slave surface are not approximately
parallel to each other
• Use of unsymmetric solver is sometimes necessary to avoid
convergence difficulties
*STEP, UNSYMM=YES
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Contact Discretization
• S-to-S discretization works best when contacting surfaces have nearly
opposing normals
• Works well for many cases involving corners
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Contact Discretization
• Surface-to-surface discretization, however, has difficulty resolving
point-to-surface contact
Slave
Point-to-surface
contact
Master
Surface-to-surface
contact
Slave
Master
Surface-to-surface formulation:
• Penetrations averaged over finite
regions
• Contact normal based on slave
surface normal
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Contact Discretization
• Supplemental edge-to-surface formulation for general contact:
• New in Abaqus/Standard 6.11; non-default in this first release
• Good for enforcing certain contacts for which surface-to-surface
formulation struggles
General contact with S-to-S formulation
• Diverges 25% into simulation
• Penetration near feature edge
• 36 increments; 317 iterations
General contact with S-to-S
and E-to-S formulations
• Runs to completion
• Good resolution of contact
• 28 increments; 130 iterations
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Contact Discretization
• Supplemental edge-to-surface formulation for general contact:
• Additional examples
Two views of
same analysis
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Contact Discretization
• Limitations of edge-to-surface in Abaqus 6.11
• 3D, solid edges only; general contact only
• Not supported in Abaqus/CAE
• Not yet active by default
• Keyword interface (like Abaqus/Explicit)
*Surface Property Assignment, Property=Feature Edge Criteria
surface_name, cut-off angle (between facet normals, in degrees)
q = +40°
Include edges
where q ≥ qcut-off
q = -90°
• Sign convention
• + for exterior angles
• - for interior angles
• q is measured in
undeformed configuration
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Edge-to-surface contact
• Internal surface “General_Contact_Edges”
• Edges of included surfaces that satisfy the feature edge criteria
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Contact Discretization
• Modeling suggestion for contact pair models:
• Supplement surface-to-surface contact pairs with node-to-surface
contact pairs involving significant feature edges
Contact surfaces
Holder
Clip
leadingEdge
*Contact Pair,
Clip, Holder
type=SURFACE
*Contact Pair, type=NODE
leadingEdge, Clip
TO
TO
SURFACE
SURFACE
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Contact Constraint Enforcement
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Contact Formulation Aspects
• Discretization
• How are constraints formed?
• For example, how to calculate gap or penetration
distances from nodal positions
• Node-to-surface or surface-to-surface
• Enforcement
• How are constraints enforced?
• For example, numerical method to resist
penetrations
• Direct (Lagrange multipliers) or penalty methods
• Evolution of discretization
• How do constraints evolve upon sliding?
• Rigorous, nonlinear evolution (―finite sliding‖) vs.
approximate (―small sliding‖)
Contact formulation
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Constraint Enforcement
• Strict enforcement
• Intuitively desirable
• Can be achieved with Lagrange multiplier method in Abaqus/Standard
• Drawbacks:
• Can make it challenging for Newton iterations to converge
• Overlapping constraints are problematic for equation solver
• Lagrange multipliers add to equation solver cost
Physically “hard” pressure vs. penetration behavior
p, contact pressure
h
h<0
No penetration:
no constraint required
No pressure
h=0
Constraint enforced:
positive contact pressure
Any pressure
possible when in
contact
h, penetration
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Constraint Enforcement
• Direct enforcement
• Lagrange multiplier method
• Constraint equations and Lagrange multipliers added to system of equations
Unconstrained system of equations
u
K
=
f
Unitless distribution
coefficients for
constraint force
Constraint equations added
K
C
BT
0
u
l
f
=
0
Vector of Lagrange multiplier degrees of
freedom (constraint forces or pressures)
• One per constraint
Ku + BTl = f
Cu = 0
Unitless constraint
coefficients
For symmetric constraints:
B=C
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Constraint Enforcement
• Penalty method
• Penalty method is a stiff approximation of hard contact
p, contact pressure
No pressure
Any pressure
possible when in
contact
p, contact pressure

No pressure
k, penalty stiffness
h, penetration
Strictly enforced hard contact
h, penetration
Penalty method approximation of hard contact
K+Kp
u
=
f
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Constraint Enforcement
• Pros and cons of penalty method
• Advantages:
• Improved convergence rates
• Better equation solver performance
• No Lagrange multiplier degree of freedom unless contact
stiffness is very high
• Good treatment of overlapping constraints
• Disadvantages:
• Small amount of penetration
• Typically insignificant
• May need to adjust penalty stiffness relative to default setting in
some cases
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Constraint Enforcement
• Default penalty stiffness
• Abaqus tries to find ―happy medium‖ between:
• Penalty stiffness too low:
• Excessive penetrations
• Penalty stiffness too high in Abaqus/Standard:
• Convergence rates degrade
• Lagrange multiplier degrees of freedom needed to avoid illconditioning
• Penalty stiffness too high in Abaqus/Explicit:
• Significant reduction in stable time increment
• Default penalty stiffness is based on representative stiffness of
underlying elements
• Scale factor applied to this representative stiffness to set default
penalty stiffness; magnitude higher in Abaqus/Standard than in
Abaqus/Explicit
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Constraint Enforcement
• Options to scale the penalty stiffness are available:
• For cases in which default penalty stiffness not suitable
• Order-of-magnitude changes recommended
• If scale factor > 100, Abaqus will automatically invoke a
variant of method that uses Lagrange multipliers to avoid
ill-conditioning issues
Keyword interface
*SURFACE INTERACTION
*SURFACE BEHAVIOR, PENALTY
penalty stiffness, clearance offset, scale factor (all optional)
:
*STEP
:
*CONTACT CONTROLS, STIFFNESS SCALE FACTOR=value
Step dependent
(careful!)
Multiplicative!
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Constraint Enforcement
• Penalty stiffness magnitude
• Stiff or blocky problems:
• The default penalty stiffness generally produces results comparable
in accuracy with those obtained with direct method
• Usually requires less memory and CPU time
• Bending-dominated problems:
• The default penalty stiffness can often be scaled back by two orders
of magnitude without any significant loss of accuracy
• Scaling back penalty stiffness for bending-dominated problems
sometimes increases convergence rate
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Constraint Enforcement
• Example
Constraint
enforcement
Maximum
penetration
Max. Mises
# Iters.
stress
Solver
FLOPs
Default
penalty
0.4% of collar
elem. dimension
6.166E4
50
2.8E10
Lagrange
multiplier
0
6.173E4
57
3.6E10
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Constraint Enforcement
• First load increment of sheet forming example
• Numerically challenging due to:
• Low-energy deformation modes for flat, unstretched sheet
• Possibility of material yielding during Newton iterations
• Even if converged solution for increment does not yield
• Dramatic change in contact status distribution
Deformable
blank
Rigid
punch
Rigid die
Components shown
separated
Actual initial configuration
(touching)
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Constraint Enforcement
• First load increment of sheet forming example (cont.)
• Convergence behavior without stabilization
Constraint
enforcement
First Increment
(without stabilization)
Lagrange
multiplier
Does not converge
Default
penalty
Does not converge
Penalty scale
factor of 10-5
Converges in 5
Newton iterations
Next steps for analysis would be to:
• Increase penalty stiffness to improve accuracy
• Easier once approximate solution is found
• Apply remaining load
Punch
Blank
Die
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Constraint Evolution upon Relative
Sliding between Bodies
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Contact Formulation Aspects
• Discretization
• How are constraints formed?
• For example, how to calculate gap or penetration
distances from nodal positions
• Node-to-surface or surface-to-surface
• Enforcement
• How are constraints enforced?
• For example, numerical method to resist
penetrations
• Direct (Lagrange multipliers) or penalty methods
• Evolution of discretization
• How do constraints evolve upon sliding?
• Rigorous, nonlinear evolution (―finite sliding‖) vs.
approximate (―small sliding‖)
Contact formulation
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Relative Sliding between Bodies
• Abaqus offers finite- and small-sliding
versions of S-to-S and N-to-S contact
formulations
• Finite-sliding formulation: General
applicability
201
206
202
203
204
205
101 102 103
104 105 106
• Point of interaction on master
surface updated using true
representation of master
surface
• Small-sliding formulation:
Approximation intended to reduce
solution cost; limited applicability
Master surface
102
• Planar representation of master
surface per slave node based
on initial configuration
• Only available for contact pairs
(and not self-contact or
Master “slide plane”
for slave node 102
general contact)
102
Possible path of
slave node 102
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Small-Sliding Approximation
• Every slave node interacts with its own local slide plane
• In 2-D/axisymmetric it is depicted as line
• Assumes that relative motion per slave node remains
small compared to:
• Local curvature of master surface (see diagrams)
• Facet sizes of master surface
• Advantage: Less nonlinearity
• Potential for reduced cost per iteration and finding a
converged solution in fewer iterations
• Disadvantage: Results can be nonphysical if relative
tangential motion does not remain small
• It is the user’s responsibility to ensure that the
assumption is not violated
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Small-Sliding Approximation
• Example of nonphysical behavior with
small-sliding formulation
• Approximately cylindrical surface
assigned to act as master surface
• Slide planes represented by white lines
in animation
• Slide planes translate with punch as it
moves to the right
• Key points:
• Small-sliding formulation can cause nonphysical results
Slave
nodes
• Obviously incorrect response in this example
• Not always obvious
• Use finite-sliding formulation if you do not want to worry about whether
small-sliding assumptions are appropriate!
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Small-Sliding Approximation
• Invoking small-sliding (contact pairs only):
*CONTACT PAIR, SMALL SLIDING
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Formulation Summary
• Good formulation characteristics (for accuracy, robustness, and generality)
• Accurate representation of surface geometry
S-to-S
• Slave surface: Not just a collection of points
• Master surface: Not approximated as flat per slave node
finite-sliding
available for S-to-S
• Geometric corrections: Reduce discretization error
• Distribution of nodal forces consistent with underlying element formulation
• Ability to satisfy ―patch tests‖ for contact
S-to-S
• Continuity in contact forces upon sliding
S-to-S
• Individual constraint stresses should oppose penetration (and sliding)
S-to-S
• Nontrivial aspect for some quadratic element types
• Avoid ―over-constraints‖ and ―under-constraints‖
master-slave roles
• Generally, number of contact constraints in an active contact region should
equal number of nodes of the more refined surface in that region
• Small amount of numerical ―softening‖
penalty method
• Robust contact search algorithm to avoid missing contacts, etc.
E-to-S
• Special treatment of feature edges
finite-sliding
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Formulation Summary
• Available formulations for general contact and contact pairs in
Abaqus/Standard
Modeling Approach
Formulation Aspect
Contact Discretization
Contact Enforcement
Constraint Evolution
upon Sliding
General Contact
Contact Pairs
Primary: Surface-to-surface
Default: Node-to-surface
Suppl.: Edge-to-surface
Optional: Surface-to-surface
Default: Penalty
N-to-S default: Direct
Optional: Direct
S-to-S default: Penalty
Finite sliding
Default: Finite sliding
Optional: Small sliding approx.
Refers to defaults for keyword input file:
• These defaults were established prior to implementation of
surface-to-surface discretization and penalty methods
• These are not the defaults for contact pairs created in
Abaqus/CAE based on initial proximity
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Formulation Summary
• Common issues when converting contact pair models to general
contact
• Most issues are related to initial overclosures
• General contact accounts for shell/membrane thickness
• Finite-sliding, node-to-surface contact pairs do not
Initial penetration if shell
thickness considered
• General contact typically considers all exposed surfaces
• Contact pairs may not be defined on some penetrated regions
• Recall clamp example
Slave surfaces of
contact pairs
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Formulation Summary
• Common issues when converting to general contact (cont.)
• Different default treatment of initial overclosures
• Contact pairs
• Initial overclosures treated as interference fits by default
• General contact
• Small initial overclosures resolved with strain-free adjustments
• Large initial overclosures assumed nonphysical/unintended
Assume only surfaces
shown with bold lines are
included in the general
contact definition
• Further discussion on next slide
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Formulation Summary
• Comments on initial overclosures (more comments later)
• User responsible for directing the treatment of initial overclosures
• Choice of whether to resolve them with or
without strains requires user judgment
• Common characteristics of interference fits
• Overclosure distance may be large
?
• Limited to specific interfaces
• Often require pair-wise attention
?
• Strain-free adjustments
• Intended to resolve small overclosures (e.g., due to faceted
representation of curved surfaces
• For small overclosures, automated algorithm can determine
which nodes to move and where to move them
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Incrementation and Newton Iterations
(Abaqus/Standard)
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Incrementation and Newton Iterations
• Newton method: Iterative method used to solve nonlinear problems
Given:
• Starting displacement, u0
―Residual
force‖ after
1st iteration
• Desired load, ―P‖
• Ability to evaluate f(u) and K(u)
I0 = f(u0)
Iteration 1
• System of eqs.
K0 Du = P – I0
• Du = ca (see fig.)
• New estimate
Iteration 2
ua = u0 + ca
• System of eqs.
Ka Du = P – Ia
• Du = cb (see fig.)
• New estimate
ub = ua + cb
Find:
• Displacement solution, us, such
that f(us) = P
magnified
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Incrementation and Newton Iterations
• The Newton method, however, is not guaranteed to converge
• Example in which Newton iterations diverge:
Load
Goal: find this point
P
Diverging!
Applied load
Displacement
Starting point
Load applied in 1 increment
• Increase the likelihood of convergence by decreasing load increment
• Use multiple load increments to achieve desired total load
Load
Load
P
P1
Displacement
Half load in 1st increment
Displacement
Remaining load in 2nd increment
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Incrementation and Newton Iterations
• Abaqus automatically adjusts the load increment size
• Goal: Find converged solution robustly and efficiently with respect to the
number of iterations
• Basic idea: Track convergence rate to determine when to increase or
decrease load increment size
• User suggests increment size; Abaqus tries to optimize it
Slow convergence
or divergence
Reduce
increment size
Convergence in few
iterations
Increase
increment size
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Incrementation and Newton Iterations
• Occasionally, may “jump across” an unstable region of loaddisplacement curve with larger increments!
Goal: find this point
Load
P
Applied load
1st iteration
estimate
Will converge
after 1 or 2
more iterations
Displacement
Starting point
Load applied in 1 increment
• Applying same total load over multiple increments would likely lead to
converge failure in this example
• Not particularly common
• Recommendation: resolve instability rather than try to ―jump past it‖
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Incrementation and Newton Iterations
• Contact causes kinks in the load vs. displacement curve
• There is a slope discontinuity upon change in contact status
• As a result, contact changes interrupt overall convergence rate tracking
Undeformed shape
3. Compress tip
2. Contact
rigid surface
1. Bend beam
P
Deformed shape
(Mises stress contours)
Challenging for
Newton method!
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Incrementation and Newton Iterations
• “Severe discontinuity iterations” (SDIs)
• An SDI is an iteration during which contact constraints change state
• Open/closed, stick/slip (active or inactive)
• The logic to adjust the increment size treats SDIs separately
Status (.sta) file
for beam contact
example:
Separate iteration
counts for SDIs and
non-SDIs
1st attempt did not
convergereduce Dt
2nd attempt at first
incr. converges
Increase Dt due to
fast convergence
Converged incr. with
contact activated
DP  (Dt/T) Pfinal
Total step
time=1.0
Trend toward larger
Dt after contact is
established
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Incrementation and Newton Iterations
• “Hard” contact pressure vs. overclosure:
Contact
pressure
Compliant
Non-compliant
“Hard” contact
Penetration
distance
Gap distance
Penetration for
“open” contacts
Tensile stress for
“closed” contacts
• Default behavior: SDIs do not block convergence
• ―Convert SDI‖: Small penetrations/tensile stresses trigger contact status
changes (and SDIs) but do not necessarily block convergence
• Without ―Convert SDI‖
• Contact status changes block convergence
• Some older contact controls (e.g., ―Automatic Tolerances) avoid contact
status changes upon small noncompliance (not recommended)
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Incrementation and Newton Iterations
Begin
increment
Increment Flowchart Schematic
1
Identify initially
active contact
constraints
2
Form and
solve system
of equations
Identify changes
in contact
constraint status
3
Newton
iterations
Determine if
Check if
4
tending toward
solution has
convergence No
converged
Yes
5
No
(Reduce increment
size and try again)
1
(At least one convergence
criterion is not satisfied)
End
Yes increment
(Within convergence
tolerances)
Determine the initial contact state at each point (closed or open)
• For first increment of a step, based on initial model state
• Otherwise, based on solution extrapolation (if any)
2•
Form the system of equations with contact constraints imposed,
then pass through the equation solver
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Incrementation and Newton Iterations
Begin
increment
Increment Flowchart Schematic
1
Identify initially
active contact
constraints
2
Form and
solve system
of equations
Identify changes
in contact
constraint status
3
Newton
iterations
Determine if
Check if
4
tending toward
solution has
convergence No
converged
Yes
5
No
(Reduce increment
size and try again)
3
(At least one convergence
criterion is not satisfied)
End
Yes increment
(Within convergence
tolerances)
Are contact pressures, clearances, frictional stresses, and sliding
increments consistent with the assumed contact state?
• Contact status changes (open/closed or stick/slip) often cause significant
changes to the system of equations
• Iterations with contact status changes are flagged as severe discontinuity
iterations (SDIs)
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Incrementation and Newton Iterations
Begin
increment
Increment Flowchart Schematic
1
Identify initially
active contact
constraints
2
Form and
solve system
of equations
Identify changes
in contact
constraint status
3
Newton
iterations
Determine if
Check if
4
tending toward
solution has
convergence No
converged
Yes
5
No
(Reduce increment
size and try again)
4
(At least one convergence
criterion is not satisfied)
End
Yes increment
(Within convergence
tolerances)
Has convergence been achieved?
• Convergence criteria ensure small force residuals, small solution
corrections, and small contact incompatibilities
5
If convergence is not achieved, is it likely to be achieved?
• Abaqus determines whether to continue iterating or to reattempt the
increment with a smaller load increment based on trends in recent
iterations
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Lecture 3 Summary
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Review of Topics Discussed in this Lecture
• Title: Numerical Methods
• Contact Formulation Aspects
• Contact Discretization
• Contact Enforcement Methods
• Contact Tracking
• Incrementation and Newton Iterations
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Contact Output and Diagnostics Tools
Lecture 4
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Overview
• Output of Contact Results
• Contact Pressure Accuracy
• Contact Diagnostics (Visual)
• Contact Diagnostics (Text)
• A high-level understanding of the numerical methods that Abaqus uses
for contact (subject of previous lecture) can be helpful for:
• Understanding diagnostic output
• Troubleshooting convergence problems
• Overcoming solution noise
• Tools are available in Abaqus/CAE to visualize contact output
• Greatly simplifies the troubleshooting process
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Output of Contact Results
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Output of Contact Results
• Output files
• Output database (.odb) file
• Used for postprocessing with Abaqus/Viewer
• By default, ODB output includes preselected variables
• Data (.dat) file
• Printed output; no output by default
• Results (.fil) file
• Used for postprocessing with third-party postprocessors; no output
by default
• Output variable types
• Nodal variables
• Whole surface variables
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Output of Contact Results
• Nodal output to the ODB file
• Default nodal contact output to ODB file includes the following variables:
• Contact stresses (CSTRESS):
• Contact pressure CPRESS
• Frictional shear stresses CSHEAR1 and CSHEAR2
• Contact displacements (CDISP):
• Contact openings: COPEN
• Accumulated relative tangential motions: CSLIP1, CSLIP2
• CSHEAR2 and CSLIP2 are provided only in three-dimensional problems
• Above output available as both field and history data
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Output of Contact Results
• Additional nodal output to .odb
• Contact nodal force vectors
(CFORCE
CNORMF & CHEARF)
• Nodal areas associated with
active contact constraints
(CNAREA)
• Contact status (CSTATUS)
• Enables contour plots of
sticking/slipping/open
status
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Output of Contact Results
• CSTATUS in shell forming example discussed earlier
• No friction defined in this model
Initial
After increasing
penalty stiffness
After first increment with
small penalty stiffness
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User-Defined Range for Ensuring Contact Opening Output
• Abaqus often does not provide COPEN values
for regions with a significant gap
• Especially in recent versions
• Motivation: Minimize contact search time
• Gap distance output is important in some cases
• Previous workaround: Define an
insignificant amount of contact damping
over a gap range of interest
• Abaqus 6.10: Surface Interaction, Tracking
Thickness=value
• COPEN output at least up to value specified
• Warning: Can degrade performance
Sphere-on-plate
example
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Output of Contact Results
• Most contact output is available on both slave and master surfaces
• Cannot view contact output on surfaces based on rigid elements types
(when used as part of a contact pair) or analytical rigid surfaces
Results obtained with
surface-to-surface
contact formulation
Uniaxial
compression
loading
Rotated to see
contact pressure on
both sides of contact
interface
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Output of Contact Results
• Self-contact results
• Values of CPRESS, CSHEAR, CNORMF, CSHEARF in output
database file represent net quantities
• Contributions while a node acts as slave in some constraints and
master in other constraints for a given self-contact definition
Displacement magnification factor
of 0.96 to facilitate visualization
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Output of Contact Results
• Contact area
• Small sliding:
• Contact area always based on reference configuration (regardless
of whether or not geometrically nonlinear effects are considered)
• Finite sliding:
• Contact area always based on the current configuration
(regardless of whether or not geometrically nonlinear effects are
considered)
• Units of contact stresses
• For most elements-based surfaces: Force per actual unit area (stress)
• Beams (2-D or 3-D): Force per unit length
• Node-based surfaces: Force per user-defined nodal area (default nodal
area = 1)
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Output of Contact Results
• Nodal contact output requests
Field
History
*OUTPUT, FIELD
*OUTPUT, HISTORY
*CONTACT OUTPUT
*CONTACT OUTPUT
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Output of Contact Results
• Whole surface output to the ODB file
• History output
Output Variable
CAREA
CFN
CFS
CMN
Description
Total area in contact
Total force vector due to contact pressure and
frictional shear stress, respectively
CMS
Total moment vector about the origin due to contact pressure
and frictional stress, respectively
CFT
Vector sum of CFN and CFS
CMT
Vector sum of CMN and CMS
XN
Coordinates of a point about which the total moment due to the
contact pressure is equal to zero
XS
Coordinates of a point about which the total moment due to the
frictional stress is equal to zero
XT
Coordinates of a point about which the total moment due to the
contact pressure and frictional stress is equal to zero
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Output of Contact Results
• Whole surface output to the ODB file
• Example: Two surfaces contacting at two locations
upper body
master surface
total force
transmitted
(patch 2)
slave surface
total force
transmitted
(patch 1)
total contact
area (patch 2)
lower body
total contact
area (patch 1)
total force = total force patch 1 + total force patch 2
total area = total area patch 1 + total area patch 2
total moment = total moment patch 1 + total moment patch 2
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Output of Contact Results
• Other types of output
• Two options are available for generating printed output that is relevant to
contact analyses
PREPRINT, CONTACT=YES
• Controls output to the printed output (.dat) file during the
preprocessing phase
• Gives details of internally generated contact elements
PRINT, CONTACT=YES
• Controls output to the message (.msg) file during the analysis
phase
• Gives details of the iteration process
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Contact Pressure Accuracy
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Contact Pressure Accuracy
• Recall discussion earlier in the seminar related to this topic
• ―Consistent force‖ distribution with surface-to-surface formulation
• Results in more accurate contact pressures than with node-tosurface formulation
Node-to-Surface Formulation
Surface-to-Surface Formulation
• Geometry corrections for curved surfaces
• Better ―input‖ to the contact formulation
improves accuracy
Master
surface
Slave
surface
Correction
factors
With geometry corrections
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Contact Pressure Accuracy
• Resolution of linearly varying contact pressure
• Enhanced in Abaqus 6.10 for models with the surface-to-surface
formulation and second-order elements
• Demonstrated in a pure bending example below
• Tied contact interface; C3D10 elements
• Order of magnitude reduction in CPRESS noise in this example
1
-1
1
-1
CPRESS noise ≈ 2% of variation in CPRESS over individual facets
(for linearly varying pressure with similar C3D10 meshes)
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Contact Pressure Accuracy
• New filtering in Abaqus 6.10EF
• Applies to surface-to-surface and node-to-surface formulations
• Generally, nice effect on solutions
• Contact stress error indicators added for Abaqus/Standard 6.11
• Hertz contact example
Maximum contact pressure
Analytical
solution
Pressure
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Contact Pressure Accuracy
Abaqus
solutions
Maximum
error
indicator
Error indicators
• Points to remember for
error indicators:
Position
• Tend to be large where local variation of base variable is more complex
than what can be captured by the mesh
• Not normalized; same units as base variable
• Not conservative or precise estimates of error
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Contact stress error indicators
• Consider error indicators for examples shown earlier:
Prior
versions
6.10EF
& 6.11
Less noise
6.11
Error indicator
Interpretation:
• Accurate prediction of maximum CPRESS
• Some uncertainty where gradient is large
but pressure is low
Prior
versions
Less noise
6.10EF
& 6.11
6.11
Error indicator
Interpretation:
• Need finer mesh to predict maximum
contact pressure and characterize local
―hot spots‖
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Contact Pressure Accuracy
• Contact stress error indicators
• Nodal variables
• Similar to CSTRESS
• Request CSTRESSERI under
*Contact Output
• Output of CPRESSERI,
CSHEAR1ERI, CSHEAR2ERI
• Supported by /CAE
• Field variable output to .odb
• Not part of Variable=Preselect
• Cannot be used to drive adaptive
remeshing
• Analytical solution has
1/r stress singularity
15,000
CPRESS
• Rigid punch example
Singularities in
analytical sol’n
CPRESS peaks
increase upon mesh
refinement
5,000
• Singularity order would be 1/r0.23
for deformable bodies of like
material (frictionless)
• Corner contact singularities are
common and their presence is
often not intuitive
CPRESSERI
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Contact Pressure Accuracy
Error indicator peaks
also increase upon
mesh refinement in
this case
Position
Singular (e.g. 1/x0.3)
• 2nd-order elements (with S-to-S contact) tend
to be more sensitive to localized effects
• Increases in local stress peaks with this
modeling approach are often misinterpreted
as numerical noise (unaware of possibility of
physical singularity)
Higher peak with linear
vs. piecewise const. fit
Stress
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Contact Pressure Accuracy
(Stress variation in element
is ≈ 1 order less than displ.)
two ―linear‖ elems.
one ―2nd-order‖ elem.
Position (x)
• FE stresses at a physical singularity site
continue to increase upon mesh refinement
Max: 8.7
Max: 15.7
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Contact Pressure Accuracy
• In actual mechanical systems:
• Slight rounding of corners and localized yielding (not included in model
description) may reduce significance of these effects
• But extra wear, etc. at these locations is likely
• Consider fillets or local yielding with a sub-modeling approach
• May be impractical to model these details in a full assembly model
• Extra degrees of freedom & iterations
• More effective to use results from a global model as boundary
conditions for a more detailed local model
Relatively small region of a
power train analysis:
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Contact Pressure Accuracy
• Stress concentration example
Second, finer mesh
Frictionless contact with rigid body
Unit pressure
on end
Symmetry
plane
Reference solution:
• Peak stress=4.3
2.3%
error
2.6% of
peak stress
0.5% error
1.7% of
peak stress
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Contact Stress Error Indicators
• “Art” of interpreting error indicators
• Documentation excerpt:
Warning: Error indicator output variables are approximate and do not
represent an accurate or conservative estimate of your solution error. The
quality of an error indicator can be particularly poor if your mesh is coarse.
The error indicator quality improves as you refine the mesh; however, you
should never interpret these variables as indicating what the value of a
solution variable would be upon further refinement of the mesh.
Error indicators do not replace need for:
• Mesh refinement studies
• Other ways that analysts gain confidence
in modeling practices
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Contact Diagnostics (Visual)
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Contact Diagnostics (Visual)
• Contact diagnostics example using Abaqus/CAE
• Reference: Example Problem 1.3.4, Deep drawing of a cylindrical cup
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Contact Diagnostics (Visual)
• Visual diagnostics available in the Visualization module of Abaqus/CAE
Step 3, Increment 6: 5 iterations (3
involve SDIs)
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Contact Diagnostics (Visual)
Constrained nodes want
to open: incompatible
contact state
Toggle on to see the locations
in the model where the contact
state is changing
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Contact Diagnostics (Visual)
Slave nodes that slip; stick/slip
messages cause SDIs only if
Lagrange friction is used or if
slip reversal occurs
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Contact Diagnostics (Visual)
Contact incompatibilities are
quantified: max force
error for constrained nodes
The contact force error is
larger than the time-average
force (=3137; will see this
shortly) — contact
incompatibility too large
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Contact Diagnostics (Visual)
Contact incompatibilities are
quantified: max penetration
error for unconstrained nodes
The maximum penetration error is
much smaller than the
displacement correction (=1.68e5)
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Contact Diagnostics (Visual)
Not only is the contact incompatibility
too large, but force equilibrium has not
been achieved either
The force residual is larger
than the time-average force,
as is the estimated contact
force error (seen previously)
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Contact Diagnostics (Visual)
Four additional iterations are required, two of which
are SDIs (involve contact incompatibilities)
In the final iteration both the contact and equilibrium
checks pass and the increment converges
Introduced in Abaqus 6.9-EF
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Contact Diagnostics (Visual)
• Internal “component surface” names appear in diagnostic messages
associated with general contact
• Previously these messages referred to the overall general contact surface
The highlighted node is in
the interior of the model
These are names of internal surfaces
associated with general contact
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Contact Diagnostics (Visual)
• To facilitate visualization
• Limit what appears in Abaqus/Viewer to the slave and/or master surface
mentioned in a diagnostic message
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Contact Diagnostics (Visual)
• Use the “Create Display Group” dialog box
• Set ―Method‖ to ―Internal sets‖ in this case
Press the
―Replace‖ button
Now the highlighted node appears in the
context of the slave surface configuration
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Contact Diagnostics (Text)
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Contact Diagnostics (Text)
• Contact diagnostics example using the message (.msg) file
• Reference: Example Problem 1.3.4, ―Deep drawing of a cylindrical cup‖
• Status (.sta) file:
SUMMARY OF JOB INFORMATION:
MONITOR NODE:
200 DOF: 2
STEP INC ATT SEVERE EQUIL TOTAL
DISCON ITERS ITERS
ITERS
1
1
1
1
1
2
2
1
1
0
1
1
3
1
1
10
0
10
3
2
1
7
1
8
3
3
1U
9
0
9
3
3
2
5
0
5
3
4
1
3
1
4
3
5
1
2
3
5
3
6
1
3
2
5
3
7
1
4
1
5
3
8
1
6
1
7
3
9
1
3
4
7
3
10
1U
4
0
4
3
10
2
7
1
8
3
11
1
3
2
5
.
.
.
TOTAL
TIME/
FREQ
1.00
2.00
2.01
2.02
2.02
2.02
2.03
2.04
2.05
2.07
2.10
2.14
2.14
2.16
2.18
STEP
TIME/LPF
INC OF
TIME/LPF
1.00
1.00
0.0100
0.0200
0.0200
0.0238
0.0294
0.0378
0.0505
0.0695
0.0979
0.141
0.141
0.157
0.181
1.000
1.000
0.01000
0.01000
0.01500
0.003750
0.005625
0.008438
0.01266
0.01898
0.02848
0.04271
0.06407
0.01602
0.02403
DOF
IF
MONITOR RIKS
0.000
0.000
-0.000600
-0.00120
-0.00120
-0.00142
-0.00176
-0.00227
-0.00303
-0.00417
-0.00588
-0.00844
-0.00844
-0.00940
-0.0108
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Contact Diagnostics (Text)
• Message file, Step 3, Increment 6:
INCREMENT
6 STARTS. ATTEMPT NUMBER
1, TIME INCREMENT
1.266E-02
CONTACT PAIR (ASURF,BSURF) NODE 167 IS NOW SLIPPING.
CONTACT PAIR (ASURF,BSURF) NODE 171 IS NOW SLIPPING.
:
:
*PRINT, CONTACT=YES causes this detailed printout.
:
(Useful for troubleshooting)
Slave nodes that slip; stick/slip
messages cause SDIs only if
Lagrange friction is used or if
slip reversal occurs
:
CONTACT PAIR (ASURF,BSURF) NODE 153 OPENS. CONTACT PRESSURE/FORCE IS -830689..
CONTACT PAIR (ASURF,BSURF) NODE 161 OPENS. CONTACT PRESSURE/FORCE IS -1.43706E+006.
CONTACT PAIR (ASURF,BSURF) NODE 165 OPENS. CONTACT PRESSURE/FORCE IS -1.03301E+006.
CONTACT PAIR (CSURF,DSURF) NODE 363 OPENS. CONTACT PRESSURE/FORCE IS -3.43767E+006.
CONTACT PAIR (ESURF,FSURF) NODE 309 IS NOW SLIPPING.
5 SEVERE DISCONTINUITIES OCCURRED DURING THIS ITERATION.
4 POINTS CHANGED FROM CLOSED TO OPEN
Due to slip reversal
1 POINTS CHANGED FROM STICKING TO SLIPPING
Incompatibilities
detected in the
assumed contact
state  SDI
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Contact Diagnostics (Text)
• Message file, Step 3, Increment 6 (cont'd):
CONVERGENCE CHECKS FOR SEVERE DISCONTINUITY ITERATION
1
MAX. PENETRATION ERROR -8.1463E-009 AT NODE 331 OF CONTACT PAIR (ESURF,FSURF)
Convergence checks
for contact state
MAX. CONTACT FORCE ERROR -4184.86 AT NODE 363 OF CONTACT PAIR (CSURF,DSURF)
THE ESTIMATED CONTACT FORCE ERROR IS LARGER THAN THE TIME-AVERAGED FORCE.
AVERAGE FORCE
5.350E+03
TIME AVG. FORCE
3.137E+03
LARGEST RESIDUAL FORCE
-1.200E+04
AT NODE
333
DOF
2
LARGEST INCREMENT OF DISP.
-7.783E-04
AT NODE
329
DOF
2
LARGEST CORRECTION TO DISP.
-1.684E-05
AT NODE
337
DOF
2
FORCE
EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.
AVERAGE MOMENT
ALL MOMENT
110.
TIME AVG. MOMENT
Not only is the contact incompatibility
too large, but force equilibrium has
not been achieved either
89.0
RESIDUALS ARE ZERO
LARGEST INCREMENT OF ROTATION
1.847E-33
AT NODE
100
DOF
6
LARGEST CORRECTION TO ROTATION
6.454E-34
AT NODE
300
DOF
6
THE MOMENT
EQUILIBRIUM EQUATIONS HAVE CONVERGED
Convergence checks
for equilibrium
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Contact Diagnostics (Text)
• Four additional iterations are required; the first two are SDIs (involve
contact incompatibilities).
• In the final iteration both the contact and equilibrium checks pass and
the increment converges
CONVERGENCE
CONVERGENCE
CONVERGENCE
CONVERGENCE
CHECKS
CHECKS
CHECKS
CHECKS
FOR
FOR
FOR
FOR
SEVERE DISCONTINUITY ITERATION
SEVERE DISCONTINUITY ITERATION
EQUILIBRIUM ITERATION
1
EQUILIBRIUM ITERATION
2
2 ...
3 ...
No SDIs in these
iterations
MAX. PENETRATION ERROR -1.24301E-015 AT NODE 331 OF CONTACT PAIR (ESURF,FSURF)
MAX. CONTACT FORCE ERROR -9.94745E-005 AT NODE 331 OF CONTACT PAIR (ESURF,FSURF)
THE CONTACT CONSTRAINTS HAVE CONVERGED.
AVERAGE
LARGEST
LARGEST
LARGEST
FORCE
5.244E+03
TIME AVG. FORCE
RESIDUAL FORCE
-1.98
AT NODE
135
INCREMENT OF DISP.
-7.809E-04
AT NODE
129
CORRECTION TO DISP.
1.063E-08
AT NODE
135
THE FORCE
EQUILIBRIUM EQUATIONS HAVE CONVERGED
AVERAGE MOMENT
109.
TIME AVG. MOMENT
ALL MOMENT
RESIDUALS ARE ZERO
LARGEST INCREMENT OF ROTATION
1.925E-33
AT NODE
100
LARGEST CORRECTION TO ROTATION
-6.933E-38
AT NODE
100
THE MOMENT
EQUILIBRIUM EQUATIONS HAVE CONVERGED
3.120E+03
DOF 1
DOF 2
DOF 2
88.8
DOF
DOF
6
6
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Lecture 4 Summary
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Review of Topics Discussed in this Lecture
• Output of Contact Results
• Contact Pressure Accuracy
• Contact Diagnostics (Visual)
• Contact Diagnostics (Text)
• Keys to obtaining accurate results
• Adequate mesh refinement
• Ability of formulations to accurately pass ―patch tests‖
• Troubleshooting problems in an analysis is facilitated by:
• Having a high-level understanding of numerical methods that
Abaqus uses for contact (subject of previous lecture)
• Using diagnostic output
• Having perspective on common sources of convergence difficulty
(further discussion in next lecture)
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Convergence Topics
Lecture 5
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Overview
• Review previous discussions related to convergence
• Static instabilities
• Unconstrained rigid body motion and negative eigenvalues
• Regularization methods
• Overconstraints
• Best practices for treating initial over closures
• Discouraging semi-obsolete features
Already Discussed
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• Newton iterations, radius of convergence, and incrementation
• Diagnostics output
• Helpful for determining location and cause of convergence problems
• Changes in contact status (open/closed and slip/stick) are characterized
as severe discontinuities by iteration control algorithm
• Strict enforcement: Change from no contact stiffness to ∞ stiffness
• Penalty enforcement: Change from no contact stiffness to finite stiffness
• Less severe
• “Smooth” contact formulation characteristics enhance convergence
• E.g., continuity in nodal contact forces upon sliding
• Surface-to-surface contact discretization is smoother than node-to-surface
contact discretization
• Also helpful for convergence:
• Smooth (and more accurate) representation of curved surfaces
• Accounting for nonsymmetric stiffness terms in equation solver
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Static Instabilities
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Static Instabilities
• Types of instabilities
• Unconstrained rigid body modes
• Geometric instabilities (snap through, etc.)
• Material instabilities (softening)
F
F
F
force
F
Desired
solution
Desired
solution
Diverging
force
Solver problem in
1st iteration due
to zero slope
Moves freely
prior to contact
After 1st Newton
iteration
displacement
displacement
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Static Instabilities
• Unconstrained rigid body motion
• Many mechanical assemblies rely on contact between bodies to
prevent unconstrained rigid body motion
• Often it is impractical or impossible to model such systems with
contact initially established
Example with initial “play”
between pin and other
components
• Without user intervention, Abaqus may report solver singularities in
the message (.msg) file :
***WARNING: SOLVER PROBLEM. NUMERICAL SINGULARITY WHEN
PROCESSING NODE 17
D.O.F. 2 RATIO = 3.93046E+16
• Often leads to slow or no convergence
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Static Instabilities
• “Negative eigenvalues”
• Nonlinear systems often experience temporary
instabilities associated with a negative tangent stiffness
for a particular incremental deformation mode
• Geometric instability (snap through)
Negative
slope
f
• Material instability (softening)
• Without intervention, Abaqus will report negative
eigenvalues in the message (.msg) file
• Often leads to slow or no convergence
d
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Static Instabilities
• Intervention approaches
• Add boundary conditions (e.g., displacement-controlled loading)
• Adjust initial contact state
• Add stabilization stiffness (damping)
• Consider inertia effects (dynamic analysis)
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Unconstrained Rigid Body Motion during Static Analysis
• Singular system of equations prior to
establishing contact
F
k
F 1
1-D representation
k
-k
-k
k
2
u1
u2
F
0
=
Determinant is 0 (singular)
• Displacement-controlled loading
prior to establishing contact avoids
the singularity
• Once contact is established, the
system of equations is also stable for
force-controlled loading
• Also true with penalty enforcement
k -k
-k k+kp
u1
u2
=
F
0
Sol‟n: u1=F/k+F/kp, u2=F/kp
u 1
k
2
u2 = ku1 Nonsingular,
sol‟n: u2=u1=u
k
F 1
k -k 0
-k
0
k 1
1 0
k
2
u1
u2
l
=
F
0
0
Nonsingular
Sol‟n: u1=F/k, u2=0, l=F
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Avoiding Unintended Initial Gaps (adjustment zone)
• Avoids some rigid-body-mode issues
• User interface for contact pairs:
Initial configuration as
specified by user
Configuration after adjustment and prior
to start of analysis: slave nodes outside
adjust bands are unaffected (some
exceptions for S-to-S formulation)
*CONTACT PAIR, INTERACTION=DRY,
ADJUST=a
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Avoiding Unintended Initial Gaps (Adjustment Zone)
• User interface for general contact in Abaqus/Standard
*Contact Initialization Data, name=adjust-1,
SEARCH ABOVE=1.E-5
*Contact Initialization Assignment
allHeads , topFlange.outer , adjust-1
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Stabilization Methods
• Artificial stiffness (“damping”)
• Preferred approaches
• Contact-based stabilization
• Small resistance to relative motion between nearby surfaces
while contact constraints are inactive
• Quite effective for stabilizing initial rigid body modes prior to
establishing contact
• Volume-based stabilization
• Adaptive stabilization throughout bodies
• Quite effective for overcoming temporary instabilities that
sometimes occur mid-analysis
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Contact-Based Stabilization
• Primarily targets cases with small initial
“play” between surfaces
• Small resistance to incremental relative
motion between nearby contact surfaces
• Resistance (stiffness) is a small fraction of
the underlying element stiffness
• Resistance is ramped to zero at end of
step by default
• Resistance is inversely proportional to the
increment size (―damping‖)
F 1
k
2
ks
k -k
-k k+ks
u1
u2
=
F
0
Nonsingular
After 1st iteration:
u1=F/k+F/ks, u2=F/ks
Likely to trigger a contact status
change for the next iteration
• Typically, minimal effect on results
• Energy dissipated by normal stabilization is nearly always insignificant
• Energy dissipated by tangential stabilization can become large if large
sliding occurs
• User interface shown on next slide
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Contact-Based Stabilization
• User controls
Use the default damping coefficient:
*CONTACT CONTROLS, STABILIZE
Scale the default damping coefficient:
*CONTACT CONTROLS, STABILIZE=<factor>
Specify the damping coefficient directly:
*CONTACT CONTROLS, STABILIZE
<damping factor>
Specify a nondefault ramp-down factor:
*CONTACT CONTROLS, STABILIZE
, <ramp-down factor>
Decrease or increase the tangential damping or set it to zero:
*CONTACT CONTROLS, STABILIZE, TANGENT FRACTION=<value>
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Contact-Based Stabilization
• User controls (cont.)
New keyword interface for general contact added in Abaqus 6.10
*CONTACT STABILIZATION
Not yet supported in Abaqus/CAE
• Specify local or global contact stabilization controls
• First step-dependent suboption of CONTACT for Abaqus/Standard
• Not active by default (with one exception to be discussed); but when activated,
the ―built-in‖ settings target temporary, initial unconstrained rigid body modes
Comments on ―built-in‖ settings:
• No tangential stabilization
• Stabilization is aggressively
ramped down over increments
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Contact-Based Stabilization
• Contact Pair Example: Joint with pin and spacer
• 105K degrees of freedom
• Four bodies, connected by contact pairs
Contact
Stabilization
No
Yes
Wallclock time
(min)
226
53
# Increments
25
18
# Iterations
145
29
Mises stress in pin
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Contact-Based Stabilization
• Special case: Initially touching surfaces for surface-to-surface
discretization
Concentrated load
• Consider the case shown where the
average gap > 0 for each slave node; thus:
• Surface-to-surface contact
constraints are initially inactive
Rigid
body
• Initial system of equations would
have no resistance to the applied load
Deformable body
• Stabilization stiffness automatically added for
such cases (even if the point of touching does not correspond to a node)
• Similar to the nondefault contact stabilization just discussed:
Stabilization stiffness is zero by the end of the step and is inversely
proportional to the increment size
• Some differences: Activated automatically, acts only in the normal
direction, and is more aggressively ramped off in early increments
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Contact-Based Stabilization
• This special form of automatic stabilization is on by default for the
finite-sliding, surface-to-surface formulation
• Cannot be applied to other formulations
• Keyword interface
• Contact pairs
*CONTACT PAIR, TYPE=SURFACE TO SURFACE,
MINIMUM DISTANCE = [YES(DEFAULT)/NO]
• General contact
*CONTACT INITIALIZATION DATA, NAME=xyz,
MINIMUM DISTANCE = [YES(DEFAULT)/NO]
*CONTACT
*CONTACT INCLUSIONS
*CONTACT INITIALIZATION ASSIGNMENT
, , xyz
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Contact-Based Stabilization
• Example
• Information from status (.sta) file for
this example is shown below
Stabilization is too low (zero)
Adequate stabilization after cutback
Stabilization is ramped too low
Adequate stabilization after cutback;
a contact constraint is now active
Good convergence behavior
despite aggressive ramping
down of stabilization stiffness
Note: This analysis does not run to completion with:
• CONTACT CONTROLS, STABILIZE: Different ramp-down of stabilization stiffness
• Node-to-surface contact: Closest point does not correspond to a slave node
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Volume-Based Stabilization
• Also referred to as “static stabilization”
• Volume proportional ―damping‖ targeting local dynamic instabilities
• User interface (see documentation for details)
STATIC, STABILIZE
• Applicable to the following
quasi-static procedures:
• Static
• Visco
• Coupled TemperatureDisplacement
• Soils, Consolidation
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Volume-Based Stabilization
• Example of a static analysis using static stabilization
Volume-Based Stabilization
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• Damping term in equilibrium equation:
cM *u  I  u   P,
quasi-velocity
mass matrix with unit density
damping factor (discussed on next page)
Effect on equations solved in each Newton-Raphson
iteration
c *

* Du
K

M
d
u

R

c
M
,
 t

Dt
Dt


Volume-Based Stabilization
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• Automatic selection of the damping factor
• Abaqus automatically calculates the damping factor c
• Varies in space and with time
• Adaptive based on convergence history and ratio of energy
dissipated by viscous damping to the total energy
• Initial damping factor is based on the following premises:
• The model’s response in the first increment of a step to which
damping is applied is stable
• Not particularly effective for stabilizing unconstrained rigid
body modes at the beginning of an analysis
• Under stable circumstances the amount of dissipated energy
should be very small
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Volume-Based Stabilization
• The amount of energy dissipation associated
with the stabilization usually provides a good
indication of the significance of stabilization on
results
Here, the total energy dissipated due
to stabilization is very small compared
to the total energies involved in
deformation
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Dynamics
• Another approach for overcoming static instabilities
is to use a dynamic procedure
• Inertia is inherently stabilizing
• Equation of motion: Mu  Cu  I  u   P.
• Abaqus provides implicit and explicit dynamics
procedures
• Implicit dynamics was enhanced in Abaqus 6.9-EF
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Explicit Dynamics Time integration
• March forward in time using the central difference method
vn-1/2
an
vn+1/2=
vn-1/2+anDt
an+1=
m-1*f(tn+1,un+1)
Main focus of increment
is finding new net force
Event
time (t)
Known solution un
un+1=
(u,v,a) up to here Find solution
for next time un+vn+1/2Dt
increment (Dt)
Requires efficient
contact search!
• No matrix inversion (lumped mass)  Each increment is fast
E.g., 1 second analysis time/increment for a 2 million element model
• Conditional stability (small Dt)  Lots of increments
E.g.,100,000 increments for a 0.1 second event
Small incremental motion simplifies
update of contact conditions
≈ 1 day
analysis
time
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Implicit Dynamics Time integration
• March forward in time with implicit time integration
Event
time (t)
Known solution Find solution
(u,v,a) up to here for next time
increment (Dt)
• Solve nonlinear implicit system of equations each time increment
• Equation solver and Newton iterations (like statics)
• The time integrators used by Abaqus/Standard are unconditional stability
• Time increment size is governed by convergence rate and accuracy
• Compared to explicit time integration:
• Higher cost per increment, but fewer increments (larger Dt)
• Possibility of lack of convergence
• Convergence criteria are very similar to statics
• Inertia has a stabilizing effect (for rigid body modes, etc.)
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Abaqus 6.9-EF Enhancements to Implicit Dynamics
• Prior to Abaqus 6.9-EF the direct-integration dynamics procedure typically used very
small time increments for contact simulations
• Often not a viable approach
• Example excerpt from status (.sta) file:
1. Not accepted due to
contact status change
2. Cut back to average
time of impact
3. “Impact” calculation
Increment number
Time increment
size
1 11 1U 0
2
2
1.28e-005 1.28e-005
1.000e-005
1 11 2
0
2
2
1.79e-005 1.79e-005
5.088e-006
1 12 1
0
2
2
1.79e-005 1.79e-005
1.000e-011
1 13 1U 0
2
2
1.79e-005 1.79e-005
1.000e-005
1 13 2
0
2
2
2.37e-005 2.37e-005
5.808e-006
1 14 1
0
2
2
2.37e-005 2.37e-005
1.000e-011
1 15 1U 0
2
2
2.37e-005 2.37e-005
1.000e-005
1 15 2
0
2
2
3.02e-005 3.02e-005
6.556e-006
1 16 1
0
2
2
3.02e-005 3.02e-005
1.000e-011
1 17 1U 0
2
2
3.02e-005 3.02e-005
1.000e-005
• Time incrementation strategies first available in Abaqus 6.9-EF
are better suited for contact analyses
Repeated
pattern
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Abaqus 6.9-EF Enhancements to Implicit Dynamics
• High-level parameter:
Default for contact models
Moderate Dissipation
Similar behavior to Abaqus 6.9;
Dynamics, Application = Transient Fidelity
remains default for noncontact models
Quasi-static
Intended for quasi-static modeling
Bouncing disc example:
1st setting (default)
2nd setting
234 solver
passes
3rd setting
1277 solver
passes
168 solver
passes
1
2
3
Kinetic Energy
Comparison
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Implicit Dynamics Enhancements in Abaqus/CAE
• Key implicit dynamics enhancements supported in Abaqus/CAE 6.10
• See Abaqus 6.10 Release Notes entry 6.2
Other choices:
Moderate Dissipation
Transient Fidelity
Quasi-static
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Abaqus 6.9-EF Enhancements to Implicit Dynamics
• “Moderate Dissipation” setting (vs. ―Transient Fidelity‖ setting)
• Some additional numerical dissipation
• Better convergence behavior for contact applications
• Fewer solver passes
• Reasons: 1. No direct enforcement of velocity and acceleration
compatibility across contact interfaces
2. No half-increment residual tolerance
3. Different parameter settings for the HHT time integrator
HHT time integrator
ut Dt  ut  Dtvt  Dt 2  12  b at  bat Dt 
vt Dt  vt  Dt1  g at  gat Dt 
 Rt Dt  Ma t Dt  1  a I  Pt Dt  a I  Pt
 a  0
1
2
b  1  a 
1
4
2
g  a
1
2
Application
setting
HHT parameters
a
b
g
Moderate
dissipation
≈-0.41
0.5
≈0.91
Transient
fidelity
-0.05
≈0.28
0.55
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Abaqus 6.9-EF Enhancements to Implicit Dynamics
• Comments on Application = Quasi-static
Wire crimping
example
• Mainly intended for cases in which a static solution is
desired but stabilizing effects of inertia are beneficial
• Unable to converge with static procedure
• Performance vs. Abaqus/Explicit is problem dependent
• Also applicable to some dynamic events
• Default amplitude type is ―ramp‖ instead of ―step‖
• Like the general static procedure
• High numerical dissipation
• Backward Euler time integrator
ut Dt  ut  Dtvt Dt
v t  Dt  vt  Dtat Dt
 Rt Dt  Ma t Dt  I  Pt Dt
Crimping
prediction
Original
configuration
• Parallel performance enhancement in Abaqus/Standard 6.10
• Removed restrictions on thread parallelization
• Affects most contact analyses run in parallel
• Influence on run-time can be quite dramatic for moderate-sized models
with many increments
Wallclock (secs.)
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Thread-Parallel Elements and Contact Search for Dynamics
2000
1000
New
Old
0
1
2
4
# CPUs (with shared memory)
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Perspectives on Implicit Dynamics (Direct Integration)
• Each Newton iteration considers a system of equations of the form
K´DU = R´
• K ́ and R ́ incorporate static terms plus inertia & damping terms
• For trapezoidal rule of time integration (a=0, b=1/4, g=1/2):
K ́= K + (4/Dt2) M (similar for other time integrators)
• Some singular modes of K (static stiffness) are not singular for K ́
• Key example: Unconstrained rigid body modes
• Stabilizing effects of inertia increase after a cut-back in the increment
size (note Dt2 in denominator)
• Inertia effects should stabilize a negative eigenvalue of K if the time
increment is small enough
• Typical entries of M are typically orders of magnitude smaller than
those of K
• Use of other stabilization methods can enable larger Dt for dynamics
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Perspectives on Implicit Dynamics (Direct Integration)
• Stiffness proportional (beta) Rayleigh damping in the material often
improves convergence behavior without significantly affecting results
• Stabilizes high-frequencies
• Whereas inertia effect on K ́ has most effect on low frequencies
• Not active by default
*Material
…
*Damping, Beta=bR
Abaqus/CAE:
Property module: material editor: Mechanical Damping: Beta: bR
This is a different ―beta‖ than the ―beta‖ associated
with HHT and Newmark time integrators!
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Perspectives on Implicit Dynamics (Direct Integration)
• Comparison to statics
• Pure static analysis is usually more efficient than quasi-static analysis
with the dynamic procedure if a model is statically stable
• Quasi-static analysis with the dynamic procedure should be more robust
• But good to supplement with other stabilization methods
• Comparison to explicit dynamics
• Cost of increments/iterations vs. number of increments/iterations
• Relative overall performance is problem dependent
• Satisfaction of residual tolerances in implicit only
• Effects of ―mass scaling‖ (the only way to scale the mass in
Abaqus/Standard is to adjust the density):
• Increases stable time increment in Abaqus/Explicit
• Increases inertia effects in both
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Static Instabilities (Summary)
• Have discussed several ways to address static instabilities
• Boundary conditions
• Avoiding unintended initial gaps
• Contact-based stabilization
• Volume-based (static) stabilization
• Dynamic analysis (accounting for inertia effects)
• Abaqus Analysis User‟s Manual contains more information on these
and other methods
• Automatic stabilization of unstable problems
• Automatic stabilization of rigid body motions in contact problems
• The Riks method
• Viscous regularization
• Contact damping
• Spring elements
• Dashpot elements
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Overconstraints
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Overview
• Review previous discussions related to convergence
• Newton iterations
• Severe discontinuities
• Desirable formulation characteristics
• Static instabilities
• Unconstrained rigid body motion and negative eigenvalues
• Regularization methods
• Overconstraints
• Best practices for treating initial overclosures
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Overconstraints
• Overconstraining the model
• Lagrange multipliers that impose
contact constraints are
indeterminate when node is
overconstrained
• Analyses will typically fail in
such cases
• This situation occurs when multiple
kinematic (boundary condition,
contact, or MPC) constraints act in
same direction on same node
• May be caused by single slave
node interacting with a number
of different master surfaces
from different contact pairs
master surface 1
slave node
master surface 2
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Overconstraints
• Abaqus automatically resolves limited
set of consistent overconstraints
• Overconstraints resolved before
analysis involve intersections of
boundary conditions, rigid bodies, and
tie constraints
• Overconstraints resolved during
analysis involve intersections of
contact interactions with boundary
conditions and tie constraints
TIE
three nodes in the
same location
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Overconstraints
• If overconstraint cannot be resolved automatically by Abaqus:
• A zero pivot warning message will typically be reported to the message
(.msg) file (by the equation solver)
• You will need to:
• Identify and remove the overconstraint manually, or
• Switch to a penalty form of constraint enforcement
• Comments on overlapping constraints enforced with a penalty method
• Usually not catastrophic
• But can degrade convergence (still try to avoid)
• Tends to become more of an issue if the penalty stiffness is greater than
the default
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Best Practices for Treating Initial
Overclosures
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Initial Overclosure
• Key question: Are the initial overclosures intended as interference fits
or unintended?
• It’s really up to the user to provide the answer to this question
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Initial Overclosure
• Common causes of initial overclosure
• Intended
• Modeling interference fit in Abaqus/Standard
• Unintended
• Shell thickness not accounted for in preprocessor
• Preprocessor error
• Discretization of curved surfaces (without geometry corrections)
CAD geometry
Mesh geometry
gap
“just touching”
overlap
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Initial Overclosure
• Default treatment
• General contact in Abaqus/Standard and Abaqus/Explicit
• Treats initial overclosures (within a given tolerance) with strain-free
adjustments by default
• Overclosures greater than specified tolerance ignored
• Alternatively, in Abaqus/Standard overclosures can be treated as
interference fits that are gradually resolved over the first step
• For contact pairs in Abaqus/Standard
• Treat initial overclosures as interference fits by default
• Resolve all interference in the first (i.e., a single) increment
• Can cause convergence difficulty because the “loading”
does not scale with the increment size
• Alternatively, overclosures can be resolved gradually or via strainfree adjustments
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Strain-Free Adjustments
• General contact in Abaqus/Standard
• By default, contact initialization
removes small initial overclosures
via stain-free adjustments
• Default tolerance based on size of
underlying element facets
• Initial gaps remain unchanged by
default adjustments
• Optionally, large initial overclosures
and initial gaps can also be adjusted
• Specify search distances above
and below surfaces
• Search above to close gaps
(discuss previously)
• Search below to increase default
overclosure tolerance
*Contact Initialization Data,
name=Init-1,
SEARCH ABOVE=distance,
SEARCH BELOW=distance
*Contact Initialization Assignment
, , Init-1
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Strain-Free Adjustments
• Warning: Only slave surface nodes are relocated
• Gross (large) adjustments can severely distort initial element shapes
• You should rely only on strain-free adjustments to resolve small initial
overclosures (relative to element dimensions)
n
Element inversion (negative volume)
will occur after strain-free adjustments
Introduced in Abaqus 6.9-EF
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Visualizing Strain-Free Adjustments
• Nodal output variable called “STRAINFREE” provided to visualize
strain-free adjustments in Abaqus/Standard
• Output variable written by default if any initial strain-free adjustments
are made
• Variable available only in the initial output frame at t=0
Symbol plot of
STRAINFREE
Initial configuration
without contact
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Visualizing Strain-Free Adjustments
• The following inconsistency exists between Abaqus/Standard and
Abaqus/Explicit with respect to strain-free adjustments:
x = xo + u
Explicit adjusts u
Standard adjusts xo
Technique in Abaqus/Viewer
Desired aspect to
visualize
Abaqus/Standard model
Abaqus/Explicit model
Nodal adjustment
vectors
Symbol plot of
STRAINFREE at t=0
Symbol plot of U at t=0
Nodal adjustment
magnitudes
Contour plot of
STRAINFREE at t=0
Contour plot of U at t=0
Adjusted configuration
Undeformed shape or
deformed shape at t=0
Deformed shape at t=0
Configuration prior to
adjustments
Substitute -STRAINFREE
for U in deformed plot (t=0)
Undeformed shape
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Visualizing Configuration Prior to Adjustments for
Abaqus/Standard
1. Create a field output variable equal to –STRAINFREE
• Abaqus/Viewer: Tools→Create Field Output→From Fields
• Choose a name for the new variable (―negStrainfree‖ in this example)
• Choose ―-‖ operator and STRAINFREE output variable
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Visualizing Configuration Prior to Adjustments for
Abaqus/Standard
2. View deformed plot based on this variable instead of U
• Abaqus/Viewer: Result→Step/Frame→Choose the ―Session Step‖
• Make a deformed plot with the new variable driving the ―displacements‖
Configuration that
appears in the plot
x = xo + negStrainfree
Configuration with
strain-free adjustments
Net effect is to subtract
strain-free adjustments
Configuration prior
to adjustments
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Interference Fit
• General contact in Abaqus/Standard
• General contact algorithm can treat
initial overclosures as interference fits
• Uses a shrink-fit method to resolve the
interference gradually over the course of
the first analysis step
Surface
SHAFT
• Stresses and strains
generated
Surface
BUMPER-EXT
*Contact Initialization Data, name=Fit-1, INTERFERENCE FIT
*Contact initialization Assignment
BUMPER-EXT, SHAFT, Fit-1
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User-Specified Interference and Clearance Distance for
General Contact in Abaqus/Standard
New to Abaqus 6.10
• High-level description:
1. The original mesh need not reflect
desired interference or
clearance distance
2. Strain-free adjustments used to
achieve user-specified
interference/clearance distance
Original mesh
geometry
After strain-free
adjustments
• Large adjustments may cause
element distortion problems
3. Followed by shrink fit during first
step to resolve interference
Middle of step
• Generating stress and strain
4. Surfaces that had interference fit
will appear compliant at end of
first step (aside from penalty
penetration)
No equivalent to this for contact pairs
End of step
User-Specified Interference and Clearance Distance for
General Contact in Abaqus/Standard
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New to Abaqus 6.10
• Keyword interface
• See Section 32.2.4 in Abaqus Analysis User’s Manual for details
• Assign a contact initialization method using the CONTACT
INITIALIZATION ASSIGNMENT option
• Specify the clearance or interference distance with the CONTACT
INITIALIZATION DATA option
• Clearance
CONTACT INITIALIZATION DATA, INITIAL
CLEARANCE=value
• Interference
CONTACT INITIALIZATION DATA, INTERFERENCE
FIT=value
• In both cases the SEARCH ABOVE and SEARCH BELOW
parameters can override the default ―capture zone‖
• Not yet supported in Abaqus/CAE
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Interference Fit
• By default, Abaqus/Standard contact
pairs treat initial overclosures as
interference fits to be resolved in the
first increment of the analysis
• However, with this approach the
amount of ―interference fit load‖
applied in this first increment is
independent of the increment size
relative to the step duration
• The full interference fit load is
applied in the first increment
• The full interference fit load is
sometimes large enough to cause the
Newton method to diverge
• Highly nonlinear response
Default behavior: Abaqus/Standard
attempts to remove entire
interference fit for contact pairs in a
single increment
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Interference Fit
• To model interference fits robustly
when using contact pairs in
Abaqus/Standard
• Generally recommended that you
specify the shrink fit option such
that the interference fit can be
resolved over multiple
increments within the first step
*CONTACT INTERFERENCE, SHRINK
slave, master
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Interference Fit
• Modeling an interference distance that differs from the initial mesh
overclosure with contact pairs
• Tricky combination of options
• Awkward, confusing, and not as accurate compared to new method
for general contact
• Process:
•
Strain-free adjustments to zero penetration
• Using ADJUST parameter
•
Ramp allowed interference from 0.0 to –h in
the first step
• h is the desired interference fit distance
• Using contact interference option
• Will appear as if a gap of distance h exists
between surfaces at end of first step
(even though contact constraints are
active)
Interference Fit
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• Interference fits and the surface-to-surface contact discretization
• Normal constraints applied along directions of slave surface normals
• Example: Boot seal contact-interference fit problem
Node-to-surface
Surface-to-surface
Rigid shaft
• For node-to-surface interference tends
to be resolved along the master facet
normals
• For surface-to-surface interference tends to be
resolved along the slave facet normals; may
cause undesirable tangential motions
If penetration is deeper than the element size, you
may need to use the node-to-surface formulation
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Discouraging Semi-Obsolete
Features
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(Semi-) obsolete contact features
• Changes in Abaqus 6.11 to discourage use of some features
• Objectives:
• Encourage best modeling practices
• Simplify Abaqus/CAE interface and primary documentation
• Facilitate code maintenance and development
• Mitigate customer frustration over disappearing features
• Summary of changes:
• Retire ―contact iterations‖ solution technique
• Limited effectiveness, difficult to maintain
• De-emphasize many contact controls
• Disallow problematic combination of features
• Node-to-surface, direct enforcement & C3D10 elements
underlying slave surface
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De-emphasize many contact controls
• Affected parameters of *Contact Controls option
• Approach, Automatic Tolerances, Friction Onset, Lagrange
Multiplier, MAXCHP, PERRMX, UERRMX
• Implications of being de-emphasized
• Removed from Abaqus/CAE dialog boxes and input file reader
• Documentation for them moved to .pdf files accessed through
Abaqus/Answer 4605
• Format of respective sections same as Analysis User’s
Manual, Keywords Manual, and Verification Manual
• Trigger warning messages during datacheck
• Continue to support these features (QC testing, etc.)
• Release Notes entry 11.8
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Review of de-emphasized contact controls
• Automatic Tolerances,
MAXCHP, PERRMX, UERRMX
• All related to avoiding contact
chattering
• Pre-date ―Convert SDI‖,
which has similar intent and
is typically superior
• Automatic Tolerances is popular among some users
• Often no longer needed
• Especially if other nondefault controls are removed
• Sometimes covering up fundamental modeling issues or bugs
• Often helpful to add contact stabilization in normal direction
• Which is unlikely to affect results
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Review of de-emphasized contact controls
• Approach
• Purpose is to stabilize initial rigid body modes
• Pre-dates the ―Stabilize‖ parameter, which is recommended
• May need to adjust gap distance over which ―Stabilize‖ acts
• Recommend setting Tangent Fraction=0.0
• Friction Onset
• Allows user to specify that friction can be neglected for increment
in which contact is newly established
• Non-default Friction Onset=Delayed setting is likely to degrade
accuracy
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Review of de-emphasized contact controls
• Lagrange Multiplier
• Controls whether Lagrange multipliers are exposed to the
equation solver (in some cases)
• Default algorithm controlling this choice is robust
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Disallow problematic combination of features
• Disallowed combination:
• Node-to-surface contact formulation
• Direct enforcement of contact constraints
• 2nd-order triangular slave faces
• This combination has historically caused:
• Convergence problems
• Extremely noisy contact stress output
• Release Notes entry 11.9
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Disallow problematic combination of features
• Uniaxial compression example
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Disallow problematic combination of features
• Unintentionally having this bad combination of features is quite
common
• Avoiding this combination
• Current recommendation
• Surface-to-surface enforcement and penalty method are
generally recommended
• Somewhat neutral on element type recommendation, but for
example C3D10(I) gives a more accurate representation of
curved surfaces than C3D10M
• Years ago
• We focused on C3D10M as an alternative to C3D10
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Lecture 5 Summary
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Review of Topics Discussed in this Lecture
• Title: Convergence Topics
• Static Instabilities
• Unconstrained rigid body motion and negative eigenvalues
• Regularization methods
• Overconstraints
• Best Practices for Treating Initial Overclosures
• Discouraging semi-obsolete features
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Discussion (Virtual Workshop)
• Pin connection example
• All three components are deformable and modeled with elements
• Small radial gap around pin initially
• Discuss how to control rigid body modes of pin
y
Pin
x
Various possible ―tools‖
• Contact stabilization
• Symmetric boundary
conditions
• Other boundary conditions
• Friction
• Distributing coupling
• …
z
x
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Discussion (Virtual Workshop)
• Pin connection example
• Shown here with contact established
• Without friction there may be little or no resistance to rotation of the pin
even after contact is established
y
Pin
x
z
x
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General Contact in Abaqus/Explicit
Lecture 6
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Overview
• Not providing as comprehensive an overview of Abaqus/Explicit
contact as we have for Abaqus/Standard contact in this seminar
• Some discussion of Abaqus/Explicit contact in previous “Lectures”
• Topics in this lecture include:
• Historical perspective on general contact
• Examples
• Unique aspects of general contact in Abaqus/Explicit
General Contact in Abaqus/Explicit
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Timeline of initial implementation
Abaqus 6.3
release
Start of
project
1999
2000
First prototype
test of G.C.
2001
Named
G.C.
2002
First car crash test
with G.C. prototype
Most /Explicit models now use G.C. instead of contact pairs
GC in Abaqus/Standard released in 2008 (6.8EF)
―AUC‖
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Contact in Abaqus/Explicit
• Explicit integration method efficiently solves extremely discontinuous
events
• Possible to solve complicated, very general, three-dimensional contact
problems with deformable bodies in Abaqus/Explicit
Courtesy of BMW*
* Gholami, T., J. Lescheticky, and R. Paßmann, ―Crashworthiness Simulation of Automobiles with Abaqus/Explicit,‖
ABAQUS Users' Conference, Munich, 2003
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Examples with multiple contact per node
• Crushing of aluminum extrusion
• Pinched shell layers
• Falling stack of blocks
• Corners
Courtesy of Alcan Mass
Transportation Systems, Zürich
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High-level comparison of G.C. in /Explicit and /Standard
• Very similar, highly-automated user interfaces
• Mostly same keywords and dialog boxes
• More options are step-dependent in Abaqus/Explicit
• Underlying contact formulations
• /Standard: Surface-to-surface (master-slave) plus edge-to-surface
• /Explicit: Node-to-surface (balanced) plus edge-to-edge
• Edge-to-edge examples that /Standard can’t yet model:
Repeat slide from Lecture 2
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High-level comparison of G.C. in /Explicit and /Standard
• Examples of differences between general contact in Abaqus/Explicit
and Abaqus/Standard
Characteristic
Abaqus/Explicit
Abaqus/Standard
Primary formulation
Node-to-surface
Surface-to-surface
Master-slave roles
Balanced master-slave
Pure master-slave
Secondary formulation
Edge-to-edge
Edge-to-surface
2-D and axisymmetric
Not available
Available
Most aspects of
contact definition
Step-dependent
Model data
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Contact constraint enforcement
• Penalty method is used by default for general contact in /Std & /Exp
• Only /Std has an alternative penalty enforcement method
• Lagrange multiplier method
• Default penalty stiffness is factor of 10 to 100 higher in /Std
• Increasing penalty stiffness tends to reduce time increment size
in /Exp
• Increasing penalty stiffness tends to degrade convergence
behavior in /Std
• Can scale penalty stiffness in /Std & /Exp
• Further discussion on next slide
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Penalty stiffness
displacement-controlled
loading
• For rare cases in which contact
penetration becomes significant, penalty
stiffness can be increased
symmetry
boundary
elastic
material
• Increase could have negative effect on
stable time increment
• Factors that can lead to increased contact
penetrations:
sides
constrained
U3=0
• Displacement-controlled loading
• Highly confined regions
• Coarse meshes
• Purely elastic response
Hertz contact problem:
Benchmark 1.1.11
default penalty
stiffness
scaled penalty
stiffness
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Penalty stiffness
• Penalty contact forces react to penetrations of previous increment in
Abaqus/Explicit
No contact force
acting this increment
Exp
fcont=kpenh
Contact normal force acting
throughout this increment is
proportional to penetration at
beginning of increment
• Contact is treated “implicitly” in Abaqus/Standard
Std
fcont=kpenh
Contact normal force for increment is
proportional to penetration at
converged configuration of increment
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Shell thickness and offsets
• Considered during penetration/gap calculations in /Std & /Exp
• Limited thickness-to-facet-dimension ratio for /Exp
• Further discussion on next slide
• /Exp does not account for moment due to friction frictional forces when
surface nodes are offset from point of contact
• No bull-nose at shell perimeters
no bull-nose
Rounded
perimeter in
/Exp
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Shell thickness
• Surface thickness reductions
• Abaqus may automatically reduce contact thickness associated with
structural elements to avoid issues of self-intersection
• If thickness is reduced, a warning is produced in the status file along
with element set WarnElemGContThickReduce
• Reducing the contact thickness of a surface may mean that contact
occurs later than expected—think of a pinched shell
• Use output variable CTHICK to contour the actual shell thickness used
for general contact
outer boundary
of node
penetration
outer boundary
of facet
outer boundary of
overall surface
reference surface
Penetration when the contact thickness
exceeds the surface facet edge length
Surface erosion
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• Available in Abaqus/Explicit (but not in /Std)
• Both surfaces involved in contact can erode
• Abaqus/Examples Manual Section 2.1.4: ―Eroding projectile impacting
eroding plate‖
• Usage discussed in next slides in context of:
• Abaqus/Examples Manual Section 2.1.3: ―Rigid projectile impacting
eroding plate‖
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Surface erosion
• Defining contact inclusions example: Projectile impacting eroding plate
1 Define an element-based surface that includes exterior and interior faces
of eroding plate
automatic free surface generation
*SURFACE, NAME=ERODE
PLATE,
PLATE, INTERIOR
automatic interior surface generation
• Here PLATE is an element set containing
all plate continuum elements
• Interior surfaces not yet supported in
Abaqus/CAE
• Create model with exterior surface
and plate element set
• Then, modify resulting input file
Surface ERODE
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Surface erosion
• Example (cont‟d): Projectile impacting eroding plate
2 Include general contact between
projectile and ―interior‖ surface
ERODE
• Surface topology will evolve to
match exterior of elements that
have not failed
*CONTACT
*CONTACT INCLUSIONS
,ERODE
Contact between default all-inclusive
element-based surface and ERODE
• Self-contact of ―interior‖ surface not
included
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Surface erosion
• Nodes attached only to eroded elements
• By default, treated as point masses that can experience contact with
intact facets
• Some additional momentum transfer
• Do not interact with other such nodes
• Alternatively, can specify *CONTACT CONTROLS ASSIGNMENT,
NODAL EROSION=YES
• In this case, excluded from contact
• See documentation for details
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Surface erosion
• Output variable STATUS
indicates whether or not an
element has failed
Failed elements removed
by default when STATUS
output is available
• STATUS = 0 for failed
elements
• STATUS = 1 for active
elements
• Abaqus/Viewer will
automatically remove failed
elements when output
database file includes
STATUS
failed
elements
Deactivate status variable
to view failed elements
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Initial overclosures
• /Explicit is not well-suited for modeling
interference fits
• Better to model with /Standard
• Contact overclosures present in the first step
are resolved with strain-free adjustments by
default
Defined mesh with overclosures
• Adjustments are to nodal displacements in
/Explicit
• In subsequent steps, no special action taken
to remove initial penetrations for newly
introduced contacts
• Penalty contact forces applied or
penetrations or, in some cases, penetrations
may be ignored
Initial increment with
overclosures resolved
Section of a bolt in a bolt hole
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Diagnostics
• Feedback on resolution of initial
overclosures
• Symbol (vector) plots of displacements (U)
at time=0.0
• Contour plots of displacements (U) at
time=0.0
• Automatically generated node sets
•
Adjusted nodes: node set
InfoNodeOverclosureAdjust
•
Nodes with unresolved initial
overclosures: node set
InfoNodeUnresolvInitOver
Symbol plot of surface adjustments
• Examine status and message file for
additional information
Contour plot of surface adjustments
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Diagnostics
• Initially crossed-crossed surfaces generally indicate geometry is wrong
• Diagnostic output provided:
• View element set WarnElemSurfaceIntersect using Display Group dialog
box
• Should be manually avoided
• Otherwise the surfaces will remain ―locked‖ together for duration of
analysis
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Wire crimping example
• For choice of model set up, “requires contact
exclusions”
• Results of wire crimping analysis with default allinclusive general contact domain shown
• Comparing results with modeling intent:
• Goal to capture behavior of deformable bodies
(grip and wires)
• Rigid bodies fully constrained
• Away from deformable bodies, rigid body
geometries are approximated
• Contact between rigid bodes not intended
• However, rigid body contact is enforced
when it occurs because both rigid bodies
are included in default contact domain
• Resulting model overconstrained
Undeformed shape
anvil-punch
penetration
Final deformed shape
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Defining General Contact
• Example (cont‟d): Wire crimping
• Crimping example with contact excluded between anvil and punch:
• Keywords interface: *CONTACT
*CONTACT INCLUSIONS, ALL EXTERIOR
*CONTACT EXCLUSIONS
ANVIL, PUNCH
• Abaqus/CAE interface:
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Defining General Contact
• Valid results produced for wire crimping problem when contact between
rigid bodies excluded
Energy history
with rigid body contact
excluded
Force displacement comparison
Contact pressure at end of analysis
with rigid body contact excluded
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General Contact for Coupled Eulerian-Lagrangian
• Same general contact user interface for CEL
• Not covering CEL in this seminar
• Nice examples:
Section 2.3.1, ―Rivet forming,‖
Abaqus 6.11 Examples Manual
Section 2.3.2, ―Impact of a water-filled
bottle,‖ Abaqus 6.11 Examples Manual
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More Features
Lecture 7
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Overview
• Finding more information about contact features and formulations
(once you get back to work)
• Abaqus Analysis User’s Manual
• Input files demonstrating features
• Contact constitutive models
• Pressure vs. overclosure
• Friction
• Cohesive contact, cracks, and related features
• High-level overview
• Indirectly modeling pressurized fluid working its way between contact
surfaces
• Pressure-penetration loading
• Other features related to contact
• Rigid bodies, tie constraints, interaction involving other physics
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Abaqus Analysis User‟s Manual
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Abaqus Analysis User‟s Manual
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Abaqus Analysis User‟s Manual
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Abaqus Analysis User‟s Manual
To find input files
demonstrating
features:
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Abaqus Analysis User‟s Manual
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Abaqus Analysis User‟s Manual
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Pressure-Overclosure Models
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Pressure-Overclosure Models
• Default physical pressure-overclosure model is “hard” contact
• Although the idealized ―hard‖ model is not always strictly enforced in the
numerical solution due to:
• Softening in the numerical constraint method
• Example: Penalty method (finite rather than ∞ constraint stiffness)
• Convergence tolerances for Newton iterations
• Example: Accept as converged despite very small negative
contact pressure
Idealized “hard” pressure vs. penetration behavior
h
h<0
No penetration:
no constraint required
p, contact pressure
h=0
Constraint enforced:
positive contact pressure
No pressure
Any pressure
possible when in
contact
h, penetration
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Pressure-Overclosure Models
• Abaqus provides alternative physical pressure-overclosure models
• Softened contact
• Exponential
• Linear
• Tabular
Motivation for usage may be:
• Physically based: surface coatings
• Numerically based: improve converge
• These models were available prior to
penalty enforcement
• Contact without separation
• Other features influencing overall contact constitutive behavior
• Breakable bonds, surface-based cohesive behavior, and crack
propagation along a contact interface
• Also influences tangential behavior
• User-defined behavior with user subroutine UINTER
• Also controls tangential behavior
• Not discussed here
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Exponential Pressure-Overclosure
exponential
p–h
relationship
p
• Contact pressure increases exponentially for
penetrations in range –c to 6c
ch

po c  h  c
e
p
 1 for  c  h  6c.

e 1 c 


p0
c
6c
• Surfaces come into contact when gap
distance is still slightly positive
• Positive contact pressure (and contact
stiffness) when surfaces are just touching
• Special treatment very close to h=c to avoid
numerical issues with very small stiffness
linear p–h
relationship
k0 
c
1
0.9999c
h
dp
dh h -0.9999 c
Sometimes used as a ―trick‖
to avoid unconstrainedrigid-body-mode issues
• Pressure-overclosure relationship is linear for
larger penetrations (to avoid numerical issues
with very large stiffness)
• Both c and po must be positive
*SURFACE INTERACTION
*SURFACE BEHAVIOR,
PRESSURE-OVERCLOSURE=exponential
c, po
po
c
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Tabular and Linear Pressure-Overclosure
• Tabular
• Input data points ( pi, hi ) to define a
piecewise linear relationship
between pressure and overclosure
• First data point is (0, h1)
• Zero slope before first data
point
pressure, p
(p2,h2)
(p3,h3)
(0,h1)
clearance, c
(pn,hn)
(pn-1,hn-1)
overclosure, h
• Monotonic increase in
successive data points: hi+1>hi,
pi+1>pi
• Constant slope after secondto-last data point
pressure, p
stiffness
• Linear
• Input single contact stiffness value
• Similar to penalty method
clearance, c
overclosure, h
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Softened Contact Nonlinearity
• Numerical treatment
• Linearized contact stiffness used for each Newton iteration
• Tolerance enforced on deviation from true pressure vs. overclosure
curve in convergence check
• Except in cases in which the slope of the pressure vs. overclosure
curve is very large, this contact stiffness is enforced without exposing
Lagrange multipliers to equation solver
1. For current pn, find kn
True curve
contact
(nonlinear)
2. Solve system of eqns., resulting
pressure
in pn+1, hn+1
Linearized
3. For current pn+1, find kn+1 and hn+1
pn + 1
contact
assoc. with pressure vs.
stiffness
overclosure curve
Incompatibility
k
n
4. Magnitude of hn+1 - hn+1
p0
error
considered in convergence check
pn
5. Continue iterations, as necessary
hn+1 hn+1
(new linearization)
c
clearance
penetration, h
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Contact-Without-Separation Model
• Useful for modeling adhesives
• This feature causes surfaces to be bonded for duration of analysis
once contact is established
• Only normal contact is affected—relative sliding still allowed
• Often used with the rough friction option (no sliding either)
• Usage sometimes numerically motivated (improve convergence)
• Syntax:
*SURFACE INTERACTION
*SURFACE BEHAVIOR, NO SEPARATION
Toggled off to invoke
NO SEPARATION
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Friction Models
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Friction
• Available friction models in Abaqus:
• Coulomb friction
• Isotropic or anisotropic
• Optional friction coefficient dependence on slip rate, pressure,
temperature, and field variables
• Linear interpolation of tabular data
• Exponential dependence on slip rate
• User subroutine FRIC_COEF
• Optional upper bound on shear stress
• “Rough” friction
• Sticking regardless of contact pressure as long as normal contact
constraint is active
• User-defined (through user subroutine FRIC or UINTER)
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Friction
• Stick/slip discontinuity for friction is similar to open/closed
discontinuity in normal direction
Contact
pressure
Gap
distance
Contact
pressure
Gap
distance
Constraints enforced
with Lagrange
multiplier method
Shear
stress
mp
Penetration
distance
Constraints enforced
with penalty method
Penetration
distance
Slip
Shear
stress
Dependence on
contact pressure
mp
Slip
Penalty method used by
default (“stick stiffness”)
Normal direction behavior
Tangential behavior
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„Stick‟ Constraint Enforcement
• Lagrange multiplier method can cause
overconstraint problems
• Such as at junctions like shown here
• Overlapping, strict constraints cause
problems for equation solver
slave
slave
t
tcrit
Slave to two
masters at corner
Dg (SLIP)
Strict enforcement of
“stick” constraints
contact normal
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Local Tangent Directions
• Are used for:
• Contact output (e.g., components of slip & shear stress)
• Anisotripic friction (different m1 and m2)
• Conventions (see Manual)
2
1
projection of
x-axis onto
surface
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Nonlinear Friction Coefficient
• Friction coefficients can be functions of:
• Equivalent slip velocity,
• Contact pressure, p
g eq  g 12  g 22
• Average surface temperature,
• Average field variable value,
• For linear interpolation of tabular data:
q
fi
q A qB
2
• If m is a function of field variables, the DEPENDENCIES parameter must
be used on the FRICTION option to specify the number of field variable
dependencies
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Nonlinear Friction Coefficient
• User subroutine FRIC_COEF (and VFRIC_COEF)
• Allows you to specify an expression for the friction coefficient
• For Abaqus/Standard, also provide expressions for derivatives
• Example: m = A (1 + B ġ + C ġ2) (1 + D p)
*
*
*SURFACE INTERACTION, NAME=name
*FRICTION, USER=COEFFICIENT,
PROPERTIES=4
A, B, C, D (substitute real numbers)
subroutine fric_coef ( fCoef, fCoefDeriv,
nBlock, nProps, nTemp, nFields, jFlags, rData,
surfInt, surfSlv, surfMst, props, slipRate, pressure, tempAvg, fieldAvg )
include „aba_param.inc‟
dimension fCoefDeriv(3)
parameter ( one = 1.d0, two=2.d0 )
m
∂m
∂ġ
∂m
∂p
∂m
∂q
fs = one + props(2)*slipRate + props(3)*slipRate**2
fp = one + props(4)*pressure
fCoef = props(1) * fs * fp
fCoefDeriv(1) = props(1) * (props(2) + two*props(3)*slipRate) * fp
fCoefDeriv(2) = props(1) * fs * props(4)
fCoefDeriv(3) = zero
return
end
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Nonlinear Friction Coefficient
• Kinetic friction model: Specific form
of friction coefficient vs. slip rate
m
• Exponential transition from a static
friction coefficient (ms) to a kinetic
friction coefficient (mk)
ms
m  mk   m s  mk  e
 dcg eq
,
where dc is the decay coefficient
m  mk   m s  mk  e
 d c g eq
mk
• Two methods for defining this model:
g eq
• Provide the static, kinetic, and
decay coefficients directly
• Use test data to fit the exponential
model
*SURFACE INTERACTION
*FRICTION, EXPONENTIAL DECAY
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“Rough” friction
• Optional behavior in which sticking conditions are always enforced
while surfaces are in contact (i.e., while normal constraints are active)
• Similar to Coulomb friction with m = 
• But if ―NO SEPARATION‖ behavior is also specified, resist relative
motion even if normal contact forces are tensile
• Idealized model has zero slip while in contact
• But small amount of slipping may occur due to numerical softening
(for penalty enforcement of sticking condition)
• Motivation for using rough friction may be physical or numerical (avoid
convergence problems)
*SURFACE INTERACTION, NAME=name
*FRICTION, ROUGH
Changing Friction Properties during an Analysis
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• Abaqus/Explicit: Assign a different named ―grouping‖ of contact properties
• Friction model is one part of a contact property grouping
―Library‖ of named groupings
of contact properties:
Property grouping i
…
Model or Step 1:
Surface pairing k
Step 2:
Surface pairing k
Property grouping j
• Abaqus/Standard
Assignment of contact property grouping (or ―surface
interaction‖) is step dependent in Abaqus/Explicit
• Modify the contact property grouping already assigned
Model definition:
Property grouping i
Surface pairing k
Step 1:
(no contact changes in this case)
Step 2:
Modify friction model
in property grouping i
Very limited step dependence per contact property
grouping (―surface interaction‖) in Abaqus/Standard
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Changing Friction Properties for Abaqus/Standard
• Keyword interface:
CHANGE FRICTION, INTERACTION=name
FRICTION
• Examples of what can be changed:
• Friction coefficient (most common)
• Gradually ramped from old value to new value over increments of
step for most step types
• Slip tolerance associated with penalty enforcement of stick conditions
(uncommon)
• Starting in Abaqus 6.10, slip tolerance transition uses same ramping
behavior as friction coefficient transition in most cases
• Previously any change was suddenly applied
m(t) = minitial+(mfinal -minitial)×A(t)
Ff (t) = Ff initial+(Ff final - Ff initial)×A(t)
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Cohesive contact, cracks, and related
features
High-level overview
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Stress Intensity Factors, Crack Growth, Delamination, etc.
• Meshing options
• Focused mesh around crack tip
• Traditional approach for evaluating SIF of stationary crack
• Cohesive elements
• Special elements with nodes on
both sides of an interface
• Surface-based cohesive behavior
• Contact constitutive model may
include adhesive behavior and
possibility of failure
• XFEM
• Discontinuities (e.g., cracks)
within elements
• Arbitrary, solution-dependent
crack path (without re-meshing)
Cohesive
elements
Interface
behavior built
into contact
model
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Stress Intensity Factor, Crack Growth, Delamination, etc.
• Methods to evaluate SIF for stationary cracks
• Focused mesh of traditional elements
• Tried and true method, although
somewhat tedious meshing
• Extended finite element method (XFEM)
• Create mesh without consideration of
crack geometry
• Then introduce crack
See Abaqus 6.10-EF
Benchmark Manual,
Section 1.16.2
See Abaqus 6.10-EF
Examples Manual,
Section 1.4.2
• Fracture/failure models
Use with cohesive
elements or contact
• Crack propagation criteria
• Critical stress ahead of crack
• Critical crack opening
displacement
• VCCT (virtual crack closure
technique)
• Crack length vs. time
Use with XFEM,
cohesive elements,
or contact
• Low-cycle fatigue based on
Paris law
Damage initiation
• Traction-separation model
• Built into constitutive model
• No need for an initial crack
traction
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Delamination, Crack Gowth, etc.
Damage evolution
―Area under curve‖ assoc.
with fracture toughness
separation
• Cohesive contact avoids the following aspects when creating model
• No separate mesh for the adhesive
• Not required to specify the undamaged traction-separation behavior
• No density associated with the adhesive (for dynamic procedures)
• Consistent specification of damage behavior
• Results often in close agreement
Crack growth example
Initial crack
Initially adhered, but
opens during analysis
Force
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Cohesive Contact vs. Cohesive Elements
Displacement
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Cohesive contact vs. cohesive elements
• Usability simplifications imply some applicability limitations
• Circumstances in which cohesive elements are recommended:
• Mesh for adherents is not adequately refined to capture adhesive
behavior
• Undamaged behavior other than ―traction-separation‖ needed
• Normal directions of contact surfaces significantly deviate from
being ―directly opposed,‖ while the cohesive remains active
T-peel example with
adhesive patches
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Cohesive elements/contact approaches vs. XFEM
• Cohesive elements/contact are applicable to situations in which
location of delamination or cracking is pre-determined
• For example, adhered interfaces
• XFEM
• Crack path is not pre-determined
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Contact Involving Surfaces Formed During XFEM Analysis
• Limited to:
• Resisting penetration upon re-closing (of cracked region) with a smallsliding contact formulation using a penalty method
• Only if a contact property is referred to in the XFEM ―enrichment‖
specification (by the user)
• What isn‟t modeled (yet)
• Contact with other surfaces
• Finite-sliding contact of re-closed region
• Friction of re-closed region
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Stabilization of Implicit Models With
Cracking/Delamination
• Stiffness degradation associated with interface failure is likely to cause
convergence difficulties in Abaqus/Standard
• Search for ―viscous regularization‖ in the Abaqus Anlaysis User’s
Manual
• Discussed in several sections
• Another tool to help mitigate these problems
• Inertia effects of dynamic analyses have stabilizing characteristics
• For example, XFEM applicable to implicit dynamic procedure
starting in Abaqus 6.10
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Pressure-Penetration Loading
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Pressure-penetration loading
• Models effects of pressurized fluid penetrating between contact surfaces
• Without directly modeling the fluid (no fluid elements)
• Similar to ―DLOAD,‖ but with an algorithm to control where the load is
applied over time
• Contact pressure threshold governs expansion of ―wetted region‖
• Available in 3D starting in Abaqus 6.10EF
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Pressure-penetration loading
• Use with contact pairs
• Refer to slave and master surfaces of contact pair
• Identify at least one slave node initially exposed to fluid
• Not yet supported with general contact
• Expansion of the “wetted region” is not instantaneous once the
pressure-penetration criterion is reached
• Current fluid pressure is ramped on over 0.001 of step time by default
• Can control magnitude of fluid pressure vs. time with an amplitude
definition
• Results may depend on time increment size
• Recommend controlling maximum time increment size to obtain
accurate results
• Wetted region does not shrink
• Even if contact pressure returns above threshold
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Pressure-penetration loading
• Air duct seal example
• Section1.1.16 of Abaqus Example Problems Manual
Pressure load (representing
fluid) has ―penetrated‖ into
contact interface
Undeformed
configuration
After moving rigid
surfaces closer
together
Response to fluid
pressure loading
Animation on
next slide
• Air duct seal example
Fluid pressure varies linearly
over static step by default (like a
DLOAD or DSLOAD would)
30
Pressure
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Pressure-penetration loading
―PPRESS‖ at
a typical point
0
0%
100%
% step completion
Ramp to current fluid pressure
after ―front‖ of wetted region
advances to include this point
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For more information…
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Rigid bodies
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Rigid Bodies and Contact
• Model a body as rigid if it is much stiffer than other
bodies with which it will come in contact
• For example, rigid bodies are commonly used to model
dies in metal forming simulations
• Include set of (regular) elements in rigid body definition
• Saves computations
• 6 degrees of freedom per rigid body (regardless of
number of nodes included in the rigid body)
• No element calculations for elements making up a
rigid body
• Analytical rigid surfaces
• For cases with 2D profiles
• Exact geometry
• Smooth
• Beneficial for convergence
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Ties
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Surface-Based Tie Constraints
• Potential applications
• Mesh-refinement transitions
• Two parts that are permanently attached
together (no chance of debonding)
• Approximation of contact interface where
user expects separation and sliding to be
nonexistent or insignificant
• Nonphysical results if such assumptions
are not valid! (User’s responsibility)
• Initialization aspects
• Position tolerances govern what regions are
actually tied
• Strain-free adjustments to achieve
compliance
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Surface-Based Tie Constraints
• Two keyword interfaces (!)
• *Tie
• Constraints are enforced by eliminating slave degrees of freedom
prior to equation solver
• Slave node tied to multiple master surfaces is problematic
• Cannot view constraint stresses
• *Contact Pair, Tied
• Constraints are enforced either with a Lagrange multiplier method or
a penalty method
• Slave DOF (and any Lagrange multipliers) are exposed to
equation solver
• Overconstraints are not as problematic with a penalty method
• Can view constraint stress (CPRESS & CSHEAR)
• Some other differences exist in details of these two implementations
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Other physics
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Other physics
• Interactions may also involve thermal, electrical, and pore fluid fields
• (If underlying elements involve these fields)
• Specify contact conduction, etc. properties
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Lecture 7 Summary
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Review of Topics Discussed in this Lecture
• Abaqus Analysis User‟s Manual
• Contact constitutive models
• Pressure-Overclosure
• Friction
• Cohesive contact, cracks, etc.
• Pressure-penetration loading
• Rigid bodies
• Tie constraints
• Other physics
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