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Williams2007.pdf
UNCLASSIFIED
Multi-scale Modeling of
Composite Material Damage:
An Overview
Todd O. Williams
Irene J. Beyerlein
Workshop on Validating of Damage Evolution Models for Composite
Materials, August 14-16, 2007
LAUR-07-5332
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Scope of Talk
• Give an overview of damage modeling approaches at the
different pertinent length scales for laminate structures
– Structural models : O(m) , structural thickness
– Meso-scale models, O(mm) , lamina thickness
– Delamination modeling
– Meso-scale constitutive models
– Material point models, O(μm – sub mm)
– Continuum (constitutive & failure surface) models
– Micromechanical models
– Deterministics
– Stochastic
• Strengths/weaknesses/validation & other considerations
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Model Connectivity
Structural Model
Delamination
Model
Meso-Scale Response
Material Point
Response/Constitutive Model
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Meso-Scale
Constitutive
Model
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Setting the Stage
• Advanced structural applications – increasingly operate in
regimes dominated by history-dependent phenomena
– Increasing use of laminated composite structures to meet demands
• To accurately model damage/history-dependent behavior
over multiple scales must:
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Explicitly couple behaviors across the different scales
Consider mesoscale directly rather than in smeared sense
Deal with complex material models
Have accurate fields representations – Nonlinear evolution
Not introduce restrictive assumptions about constitutive
behavior/models and types of damage states
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Setting the Stage
• To model damage/failure traverse all realms of behavior:
– Elastic
– Viscoelastic/viscoplastic
– Damage initiation – Types of damage?
» Damage growth – More types of damage?
» Failure
• Interactions of different mechanisms at each & over all
the different length scales can result in non-intuitive
behaviors
• Complex loading states
• Strain rate : Static, Intermediate, Dynamic
– Shock : Wave propagation, strong field gradients
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Structural Modeling
• What is full range of structural response characteristics expected, i.e.
what need to be incorporated in the structural theory?
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Static vs. Dynamic behavior
Vibration modes
Bending/extension
Degree of deformation
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Small rotation/small strain – Geometric linearity
Moderate rotation/small strain – Von Karman assumption
Large rotation/small strain
Finite deformations (large rotations/large deformations/large strains)
– Buckling
• What are the structural boundary conditions?
– Dirichlet, Neumann, Robin (mixed) B.C.s
– Simply supported, clamped, etc
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Structural Modeling
• Traditional (3D) Finite Elements
– Strengths
– Flexible set up/solution of problem – Available tools for
meshing/analysis
– Well proven – Extensive application to many problems
– Can handle complex constitutive models
– Delamination can be handled using various types of cracking
analyses - Cohesive zone models, VCCT, etc.
– Weaknesses
– Typically uses lower order elements in practice – Use more
elements?
– Locking/Element aspect ratio
– Lower order elements
– Computational efficiency for many lamina
– Most current practical forms have discontinuous fields at interfaces
– Implications for evolution of history-dependent effects
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– Cracking only between elements
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Structural Modeling
• Plate/Shell Theories
– Smeared/Equivalent Single Layer
– Strengths
– Global responses ok for large plate aspect ratios ( > 20)
» Vibration modes
» Bending/extension
– Computationally efficient
– Weaknesses
– Can’t provide accurate representations of local fields – Inaccurate
estimates for evolution of history-dependent effects/damage/failure in
general loading situations
– Can’t incorporate delamination effects
– Some versions don’t go to correct limits (thick/thin plate limits)
– Discontinuous tractions at interfaces
– Often limited types of boundary conditions on top/bottom surfaces
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Structural Modeling
• Plate/Shell Theories (cont’d)
– Discrete layer/Zig-Zag
– Strengths
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Can provide very accurate estimates for local fields
Can handle complex constitutive theories (not Zig-Zag theories)
Can incorporate delamination thru CZM, VCCT, etc
Approach satisfaction of interfacial continuity as order increases
– Weaknesses
– Accurate solutions - Computationally demanding
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Structural Modeling
• Plate/shell theories
– Multiscale theories – Global/Local fields
– Strengths
Can provide very accurate estimates for local fields
Can handle complex constitutive theories (not Zig-Zag theories)
Can incorporate delamination thru CZM, VCCT, etc
Potentially more computationally efficient than discrete layer theories
» Mix global orders and local orders to obtain optimal efficiency
– Can satisfy interfacial constraints exactly (GMSST)
– Framework from which to obtain ESL, DL, as well as global/local
– Transition from multiscale to global only analysis w/in surface of
plate/shell
» Obtain accurate results in critical regions and less accurate results
in regions far away
» Enhanced computational efficiency for entire solution
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– Weaknesses
– More computationally demanding that smeared theories
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Structual Modeling
• FE application of plate/shell theories
– Easier mesh generation than 3D Finite Elements
– Computationally more efficient than 3D FE due to separation of
inplane and through thickness integration
– Locking/Aspect ratio issues still present (inplane)
– Some FE implementations of plate theory do not go to the correct
limits (Classical FE/FSDT locks for thin plates, unlike FE/CLT)
• Can implement plate/shell theories in other types of
numerical strategies
– Particle Methods
– Etc.
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Structural Modeling – V&V Issues
• Can carry out initial V&V w/in context of exact solutions
for boundary value problems (BVPs)
– Use of exact solutions eliminates uncertainty issues
– What BVPs most appropriate/most demanding?
– Types of B.C.s – Cylindrical bending, etc
– Types of layups – Monolithic, Cross ply, angle ply, general layup
– Types of material behavior (currently almost exclusively elastic
material behavior)
– Need to incorporate inelastic effects
– Loading states (currently mostly static BVPs)
– Need BVPs for dynamic effects
• Comparison w/other analysis techniques for some
problem set
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Structural Modeling – V&V Issues
• Comparison w/experimental data for structural response
– Introduces the need to quantify uncertainty in material
behavior/constitutive theories
– Material consistency/uniformity
– Identification of constitutive model parameters : Extra work/money
• Appropriate combination of the above comparisons?
• Statistical issues
– Variability of material properties
– Fiber alignments
– Gaps between tows
– Variability of lamina thickness
– Variability of interlaminar regions
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Meso-Scale Modeling
• Types of failure mechanisms
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Ply cracking/splitting
Delamination
Sublaminate buckling
Crushing
Kink band formation
Localization of failure
Interactions between mechanisms
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Meso-Scale Modeling
• Models for delamination
– Cohesive zone models (CZMs) - Relates interfacial tractions to
displacement discontinuities
– Strengths
– Can predict initiation and growth w/o a priori assumptions about cracks
– Can formulate using internal state variable formalism
Variety of (coupled) history-dependent effects
– Can be implemented into many types of numerical strategies
» Applicable to complex structures subjected to complex loading states
– Direct connection to fracture mechanics
– Weaknesses
– Currently accurate assessments tied to element size in FE
» Computational efficiency (unpublished work at LANL shows how to
eliminate this constraint)
– Actual shape of the CZM may not be important – Uniqueness?
– Characterization data can be hard to obtain
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Meso-Scale Modeling
• Models for delamination
– Fracture Mechanics based analyses : LEFM, VCCT, etc.
– General Strengths
– Large body of work
– Different types of growth criteria : SIF, SERR, etc.
– Some versions of these techniques can handle complex constitutive
models for material behavior
– General weaknesses
– Assumptions about cracks
» Number of cracks
» Location of crack(s)
» Size of crack(s)
» Can be difficult to determine direction of growth/mode separation
– Potential length scale issues in composites (process zone size)
– Application to complex structures subjected to complex loading states
can be difficult
– Characterization data can be hard to obtain
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Meso-Scale Modeling
• Meso-scale (lamina scale) continuum damage modeling
– Assumes uniform stress/strain states within lamina
– Thermodynamically derived constitutive relations for lamina
behavior : Internal state variable (ISV) formalism
– Strengths
– Computationally efficient since no field variation through thickness
– History-dependent behavior predicted :
– Can incorporate many types of (smeared) effects: Viscoplasticity,
Cracking, Etc.
– Weaknesses
– Accuracy of smeared assumption
– Variation from mean fields
– Static vs. Dyn. loading states : Dyn. – Potentially strong grad. w/in lamina
– Characterization/interpretations of model parameters
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Meso-Scale Modeling – V&V Issues
• How to uniquely validate a given meso-scale fracture
model since typically have material effects influencing
behavior
– Multiple phenomena interacting at lower length scales
– Complex, 3D constitutive models
• Statistical issues
– Sensitivity of the predictions to variations in the model parameters
– Variations in model parameters : Variability in experimental
data/material behavior: Elastic properties, damage
location/localization, strength, etc.
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Material Point Modeling
• (Some) General requirements for Material Models
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Processing effects
Changing strain rates (static to dynamic)
Changing load paths (monotonic vs cyclic vs complex)
Changing temperatures rates and paths
Coupling between mechanical, thermal, and moisture (and chemical and
electrical?) effects
Aging
Influence of microstructure : Interactions between the
constituents/interfaces
Types and evolution of damage : Appropriate underlying physics – Many
types at once
Interactions between the different effects
• Pick some?
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Material Point Modeling
• Large number of damage mechanisms
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Debonding of constituents
Micro-buckling/kinking of constituents
History-dependent deformations within constituents
Void initial/growth/coalescence
Fiber bridging
Fiber or matrix damage/cracking
Others?
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Material Point Modeling
• Two types of theories : Continuum & Micromechanical
– Continuum level theories :
– Consider material behavior at macroscopic level as function of
current state
– Thermodynamically based OR Empirically postulated
– Many types : LEFM, Weibull Strength of brittle materials,
Phenomenological failure theories, Phenomenological constitutive
theories
– Micromechanical theories :
– Directly consider the material microstructure and the phase
behaviors to predict both macroscopic and microscopic responses
– Homogenization based theories
Deterministic vs stochastic
– Direct micromechanical analyzes
– Both types of models assume scale separation
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Material Point Modeling – Continuum Theories
• Failure surface models
– Many types – Max. strain/stress, Tsai-Hill, Polynomial Tensor, etc.
– Range from simple to fairly complex
– World-wide failure exercise discusses formulations and
capabilities of many leading theories of this type
– Strengths
– Computationally efficient
– Easily implemented in various types of numerical strategies
– Useful for examining trends in many possibilities
– Weaknesses
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Independent of material constitutive behavior – Not history-dependent
Phenomenological/Empirical
Predictions : Initial damage state vs final damage state?
Validity in coupled loading states
Identification of model parameters
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Material Point Modeling – Continuum Theories
• Macroscopic constitutive theories
– Material behavior determined by current state
– Basis (often) rests on thermo-dynamic constraints/relations
although have empirical developments as well
– 1st and 2nd law
– Thermo-dynamic potentials
– Postulates types/evolution/interactions of history-dependent
effects – Internal State Variables (ISV)
– Only two observable external state variables : Strain and Temperature
– ISVs inferred/postulated : Attempt to account for changes in internal
state/structure
– Gives macroscopic response only
– Examples – Viscoelastic theories, Incremental plasticity, BodnerPartom viscoplastic theory, Continuum Damage Mechanics (scalar
and tensor forms), etc.
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Material Point Modeling – Continuum Theories
• Macroscopic constitutive theories
– Strengths
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Computationally efficient
Large historical body of work
Flexible formulational framework
Can couple many types of physical mechanisms interactively
Can be/have been implemented into many numerical schemes
Characterization of model parameters can be simpler than for
micromechanical models (no interface parameters needed)
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Material Point Modeling – Continuum Theories
• Macroscopic constitutive theories
– Weaknesses
– No direct account of microstructure
– No direct account of fundamental response mechanisms/interactions
– Postulates types/evolution/interactions of history-dependent effects
– Only two observable state variables : Strain and Temperature
– Internal state variables inferred/postulated
– No generally accepted set of ISVs for given class of materials
» Some art in chosing set of ISVs, the thermodynamic potentials, and the
evolution equations for ISVs
– Need to reformulate if postulated physics changes
– Complex models – Large numbers of ISVs
– More difficult to integrate due to many time scales
– More difficult to characterize model parameters
– More difficult to interpret meaning of different parameters
– More sensitive to changes in the data?
– Development for anisotropic materials more complex than for isotropic
materials
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Material Point Modeling – Micromech. Theories
• Micromechanical theories
– General Strengths
– Direct insight into microstructural effects
– Direct insight into fundamental response mechanisms and their
relative importance
– Gives both micro and macro responses
– Can incorporate physics as necessary
– Handles anisotropy naturally
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Material Point Modeling – Micromech. Theories
• Micromechanical theories
– General Weaknesses
– How much microstructural info is enough?
– Definition of appropriate microstructure (RVE/Unit Cell)
– Mean fields vs. detailed microstructural info
– Type of physics incorporated influences predictions
– More characterization info req’d than continuum constitutive theories
– Phase properties,
– Interface properties (Often very difficult to obtain accurately)
– Accurate simulations
– More computational state variables to carry in analysis
» More memory intensive
» More computationally demanding (than most continuum level
theories)
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Material Point Modeling – V&V Issues
• Interpretation of Exp. Data – What is the appropriate
underlying physics?
• Material characterization –
– Simple tests – Sufficiency/uniqueness?
– Elimination of structural size effects to obtain pure material
behavior
– Nonlinear, multivariable optimization for advanced continuum
level models
– Sensitivities of the models to variation in the parameters
– Influence of experimental data variability
• Satisfaction of the scale separation assumption?
– Under strong dynamic loading assumption may not be satisfied.
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Summary/Final Considerations
• Many required component models required to analyze
multiscale BVPs
– Non-intuitive interactions between different physics and different
component models can occur
• Questions that need to be addressed within the context of a
given modeling framework:
– Accuracy
– How is this judged?
– What is good enough?: Trends/Engineering analyses vs. accurate
predictive analyses? Probably require both to ensure safety.
– Accuracy vs. computational efficiency vs. modeling framework/
complexity vs. computational resources – Trade offs
– Where’s the uncertainty and how is it propagating thru analysis?
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Not so Bleak – Dedicated to Frank Addessio
• Outlined many problems but is the picture so bleak? NO.
– Any approach is a optimization of different considerations : Must
balance needs/capabilities
– Identify size of critical regions in structure?
– Is computational efficiency more important than accuracy or vice
versa or is this even a necessary questions?
– Can different techniques be combined to enhance both accuracy and
OVERALL computational efficiency?
» Use meso-scale constitutive models away from critical area while
use continuum or micromechanical constitutive models in critical
area?
– Can new techniques be introduced?
» Multiscale analysis with global/local to global only transitions can
enhance comp. efficiency.
– Are trends good enough or do you need predictive capabilities?
» A lot of experimental data vs. little experimental data?
– Computational resources are getting more capable all the time.
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– How much time to you have to do the implementations?
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Not so Bleak
• Additional considerations
– Computational resources are getting more capable all the time.
– Parallel processing makes some things more feasible.
– How much time to you have to do the implementations?
– How much expertise required to do the implementations?
– Modeling is getting more complex → Team efforts becoming more
important
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