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Altidis2005-ANSYSUsersGroup-HyperelasticMaterials+
Midwest ANSYS Users Group
May 18, 2005
Analyzing Hyperelastic Materials
w/ Some Practical Considerations
Prepared by: Paris Altidis; Borg Warner
Updated by: Vince Adams; IMPACT
©2004 – IMPACT Engineering Solutions, Inc.
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What Is a Hyperelastic Material ?
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Can experience large strains (up to 500%) and most of it - if
not all - is recoverable.
Rubber is a hyperelastic material; behavior is reminiscent
of a viscous fluid during its processing to shape.
The vulcanization and/or curing of rubber type materials
causes their polymer chains to crosslink which allows the
material to fully recover from elastic deformations.
Load-Extension behavior is nonlinear
Nearly incompressible – Exception is some rubber foam
materials where large volume changes can be achieved.
Low Cost / Flexible / Resilient - Work in many environments
(moisture, pressure, heat)
www.impactengsol.com
©2005 – IMPACT Engineering Solutions, Inc.
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Where are Hyperelastic Materials Used?
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Automotive (Tires, Belts, Hoses, Mounts)
Aerospace (Remember the failed O-ring on the
Space Shuttle ??)
Biomedical/Dental Industries (artificial organs,
wheelchairs, implantable surgical devices)
Packaging (Styrofoam)
Sports (Equipment safety, Shoes, Helmets)
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©2005 – IMPACT Engineering Solutions, Inc.
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Available Hyperelastic Material Models in
ANSYS 9.0
Mooney-Rivlin, Polynomial Form, NeoHookean, Ogden Potential, Arruda-Boyce,
Gent, Yeoh
? For special apps like foam:
Use Blatz-Ko and Ogden Compressible Foam
?
www.impactengsol.com
©2005 – IMPACT Engineering Solutions, Inc.
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Beyond the available models in ANSYS 9.0
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User-Programmable Features (UPFs) are available
to code your own material model.
Currently available UPFs for hyperelasticity use
HYPERxx types of elements.
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©2005 – IMPACT Engineering Solutions, Inc.
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Material Modeling Basics…
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A poor material model will
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Minimum Data: Uniaxial tension
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Prevent your FE model from running
MOST likely will give you erroneous results and you will not even know it….
Try a NeoHookean Material
Best Scenario: Uniaxial AND Biaxial Tension + Pure Shear.
Do a Curve Fit and plot both test and fitted data on same plot.
Chapter 4 Structures with Material Nonlinearities in ANSYS
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Figures 4.16 and 4.17 give you all the available AND equivalent testing modes
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©2005 – IMPACT Engineering Solutions, Inc.
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Material Modeling Basics…
Figure 4.16 – Deformation Modes
Source: ANSYS 9.0 Theory – Chapter 4.6
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©2005 – IMPACT Engineering Solutions, Inc.
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Material Modeling Basics…
Figure 4.17 – Equivalent testing modes
Source: ANSYS 9.0 Theory – Chapter 4.6
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©2005 – IMPACT Engineering Solutions, Inc.
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Equibiaxial vs. Compression Testing
• Pure Compression Requires:
• Uniaxial Loading
• No Lateral Constraints
• i.e. No Friction
Friction Affects Compression Test Data
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©2005 – IMPACT Engineering Solutions, Inc.
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Equibiaxial vs. Compression Testing
While not intuitive, Equibiaxial testing gives same
response as pure compression
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Observations on Material Testing
1. The stress strain function for the 1st time an elastomer is strained
is never again repeated. It is a unique event.
2. The stress strain function does stabilize after between 3 and 20
repetitions for most elastomers.
3. The stress strain function will again change significantly if the
material experiences strains greater than the previous stabilized
level. In general, the stress strain function is sensitive to the
maximum strain ever experienced.
4. The stress strain function of the material while increasing strain is
different than the stress strain function of the material while
decreasing strain.
5. After the initial straining, the material does not return to zero strain
at zero stress. There is some degree of permanent deformation.
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Cyclic Damage and Mullins Effect
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Limitations of Hyperelastic Mat’l Models
Most material models only allow the analyst to describe only a subset of the
structural properties of elastomers. In the Mooney-Rivlin and Ogden
formulations:
1. The stress strain functions in the model are stable. They do not change
with repetitive loading. The material model does not differentiate between a
1st time strain and a 100th time straining of the part under analysis.
2. There is no provision to alter the stress strain description in the material
model based on the maximum strains experienced.
3. The stress strain function is fully reversible so that increasing strains and
decreasing strains use the same stress strain function. Loading and
unloading the part under analysis is the same.
4. The models treat the material as perfectly elastic meaning that there is no
provision for permanent strain deformation. Zero stress is always zero strain.
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©2005 – IMPACT Engineering Solutions, Inc.
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Where is Material Tested ??
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Always test your material with loading that is similar to the
actual application
Contact Axel Products or DatapointLabs for guidelines on
what is required.
Visit their websites and RTFM (Read Their Fantastic
Methods). Many papers can be downloaded for reference.
www.axelproducts.com
www.datapointlabs.com
www.impactengsol.com
©2005 – IMPACT Engineering Solutions, Inc.
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Curve Fitting of Hyperelastic Parameters
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The recommended method is the ANSYS Curve Fitting Wizard.
Hardcore users: Use APDL to create your own scripts for the curve
fitting portion and post-processing.
For a decent curve fit using the M-R models, you need 2X the number
of M-R Parameters.
Papers on www.ansys.net provide in-depth info on these
techniques… Most will be posted to the MAG site
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©2005 – IMPACT Engineering Solutions, Inc.
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Testing Procedures…
Source http://www.polymerfem.com > Surveys
TIP: DEPENDING ON YOUR DESIGN/APPLICATION NEEDS ANY OR ALL
MAY BE REQUIRED FOR THE MATERIAL AT HAND
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©2005 – IMPACT Engineering Solutions, Inc.
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2-P Mooney-Rivlin vs. Shore Hardness
How good is it ?
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Has been seen in ANSYS and
other user groups
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ONLY For Reference
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Experience has shown that it is
not consistent for ALL GRADES
and TYPES of hyperelastic
materials.
Worth using it in ANSYS as a firstpass analysis ??
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I’d rather test the material at
hand in tension at least.
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©2005 – IMPACT Engineering Solutions, Inc.
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2-P Mooney-Rivlin vs. Shore Hardness
E
psi
176.61
177.045
179.22
183.135
189.225
196.62
205.755
215.76
227.505
239.685
252.735
266.655
281.445
296.67
312.33
328.425
344.955
361.92
379.32
397.59
415.86
434.565
453.705
473.715
494.16
515.475
537.66
560.715
585.075
610.305
637.275
665.985
696
728.625
762.99
799.965
C10
psi
23.49
23.635
23.925
24.36
25.23
26.245
27.405
28.71
30.305
31.9
33.64
35.525
37.555
39.585
41.615
43.79
45.965
48.285
50.605
53.07
55.39
58
60.465
63.22
65.83
68.73
71.63
74.82
78.01
81.345
84.97
88.74
92.8
97.15
101.79
106.72
C01
psi
5.945
5.945
5.945
6.09
6.38
6.525
6.815
7.25
7.54
7.975
8.41
8.845
9.425
9.86
10.44
11.02
11.455
12.035
12.615
13.195
13.92
14.5
15.08
15.805
16.53
17.11
17.98
18.705
19.575
20.3
21.315
22.185
23.2
24.36
25.375
26.68
Mooney Coefficients
120
y = 0.1333x
100
Mooney Coefficients, psi
Shore-A
[°]
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44
45
46
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49
50
51
52
53
54
55
56
57
58
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60
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63
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65
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C10
C01
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Linear (C10)
Linear (C01)
60
40
y = 0.0333x
20
0
0
100
200
300
400
500
600
700
800
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Young's Modulus, psi
From Waltz (XANSYS)
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©2005 – IMPACT Engineering Solutions, Inc.
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2-P Mooney-Rivlin vs. Shore Hardness
E (psi) = 11.427*A -0.4445*A^2 + 0.0071*A^3 Lindemann (XANSYS)
From E. F. Gobel, Rubber Springs Design, John Wiley, New York, 1978.
1400
Young's Modulus (PSI)
1200
1000
800
600
400
200
0
20
30
40
50
60
70
80
90
100
Hardness (Shore A)
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©2005 – IMPACT Engineering Solutions, Inc.
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2-P Mooney-Rivlin vs. Shore Hardness
Comparison of Fitted Data
1200
Young's Modulus, psi.
Waltz
1000
Shore A
35
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45
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55
60
65
70
Waltz
172.75
205.58
255.84
324.42
412.23
520.16
649.12
800.00
Lindemann
159.85
200.28
261.09
347.60
465.14
619.02
814.58
1057.14
Gobel
154.42
198.56
244.15
291.63
342.36
398.58
463.45
541.01
Lindemann
Gobel
800
600
400
200
0
20
30
40
50
60
70
80
Hardness, Shore A
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©2005 – IMPACT Engineering Solutions, Inc.
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Material Model Recommendations
Material
Hyperelastic Model
Acrylate-butadiene rubber
Neo-Hookean
Chloroprene Rubber
Arruda-Boyce / Yeoh
Natural Rubber (55 pph CB)
Yeoh
Nitrile Rubber
Neo-Hookean
Silicon Rubber
Arruda-Boyce
Viton
Arruda-Boyce
Source http://www.polymerfem.com
Other material models from the same source may be used in ANSYS
via UPFs.
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©2005 – IMPACT Engineering Solutions, Inc.
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Example of O-Ring Compression
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©2005 – IMPACT Engineering Solutions, Inc.
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Example of O-Ring Compression
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Scope: The performance of an O-Ring (used in a medical device)
during assembly as a seal needs to be analyzed and the contact
forces to the mating parts be extracted.
Element Type: PLANE182 Axisymmetric (Keyopt(1)=0 Full
integration with B-bar method (No Hourglass control)
Materials: O-Ring: Hyperelastic Material (Other grade information
not available); All other parts: Steel
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©2005 – IMPACT Engineering Solutions, Inc.
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Example of O-Ring Compression
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Example of O-Ring Compression
Step 1: The lack of information about the material would not allow any guessing
(BAD MOVE). So, material tested by Axel products as shown below.
Step 2: Curve fitted to 9P M-R Model (BETTER ) (method APDL)
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©2005 – IMPACT Engineering Solutions, Inc.
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Why a 9P Mooney-Rivlin Model
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Better Fit for the strain range
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A 5-P might have worked just as well
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A Curve fit of ALL Available mat. Models and parameters were not
feasible/available at the time. (BEST CHOICE )
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The Assembly as Designed
Guess where the Solution bombed out due to highly distorted Elements.
(~ 25% into final loadstep – after preliminary contact resolution).
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The assembly as Modified to help in the Convergence
TIP : Use rounded corners in areas where the soft material gets (or is
expected to become) highly distorted and causes shear locking and
hourglassing. (Rick?)
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©2005 – IMPACT Engineering Solutions, Inc.
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Problem Solved !!
Used a Different color
to monitor the change
in orientation of all
points of interest
during the animation
process
/pnum,mat ! Plot Element by material ONLY
/num,2
! Colors only
esel,,type,,1,2 ! Select Solid Elements
/nfor,on
! Turn on nodal Forces
Pldisp
! Show Displacement plot
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©2005 – IMPACT Engineering Solutions, Inc.
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Lessons Learned…
• The use of the rounded Fillet helped
(read: saved me) in completing the
O-Ring assembly.
• Mesh deformation is acceptable.
• Contact resolution w/ mating parts as expected.
• Orientation of “monitor” elements indicate lack of
friction at the contact.
• Next iteration should incorporate friction
• Did Rich tell you about friction in contact
pairs ??
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©2005 – IMPACT Engineering Solutions, Inc.
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Solution with Friction Added…
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Another O-Ring Case Study…
2 Parameter Mooney-Rivlin
Model Used
C10=107.18, C01=26.8
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©2005 – IMPACT Engineering Solutions, Inc.
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Hourglassing
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Hourglassing occurs when there is compression in the material.
Hourglass-shaped elements can propagate through the mesh IF
THERE ARE LESS THAN 2 ROWS OF ELEMENTS IN EACH
DIRECTION.
Hourglassing IS NOT LIMITED to full integration elements. Use the
wrong Stiffness factor w/ the Uniform Reduced Integration method
and you’ll see it….
Think of it as “Rubber Turbulence” as the deformation change is
rapid and violent.
In reality, Hourglassing DOES NOT EXIST. Combination of material
model, geometry, mesh density and element selection can induce
Hourglassing in hyperelastic materials.
Use full scale plot to see Hourglassing effects.
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©2005 – IMPACT Engineering Solutions, Inc.
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Hourglassing
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Elements Supporting Hourglass control : Plane182/183, Solid
164 / 185 / 186 / 45
Use HGSTF Real Constant to Specify the Hourglass stiffness
scaling factor
However, the artificial energy introduced to control the
hourglass effect may affect solution accuracy adversely.
? Don’t just increase the Stiffness 10% for every successive
iteration
? Bump it up to some high number and then back off
? Chances are ANSYS will solve FASTER using a HIGH
HGSTF rather than a LOW and Gradually increasing value.
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©2005 – IMPACT Engineering Solutions, Inc.
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Hourglassing
CAUTION:
Introducing the HGSTF changes the the problem.
(Especially if the deformation is Bending Dominated)
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Compare the total energy (SENE) to the artificial energy (AENE)
that is being introduced by the hourglass stiffness.
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If the Ratio SENE / AENE is < 5 % the solution is acceptable.
More than 5 % ?? Refine the mesh OR reduce the HGSTF.
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©2005 – IMPACT Engineering Solutions, Inc.
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Wisdom on Hyperelastic Materials from
XANSYS - THE School of Hard Knocks
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NEVER ask a forum member to give you their material data. Yes, it
cost $ to test but this is not the area to cut corners. How do you know
the material is made from the same stuff ?? (grade, processing etc.)
The term “Strain” in hyperelastic materials is replaced by “Stretch”.
The first and second invariants of M-R and other models are based
on Stretch Ratios. The principal stretch ratio = 1 + eng. Strain.
Therefore, the test data you obtain are Engineering and NOT True
Stress and Strain.
Use the more comprehensive TB,Hyper,,option instead of
TB,Mooney which is for HYPER56/58 elements.
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©2005 – IMPACT Engineering Solutions, Inc.
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Wisdom on Hyperelastic Materials from
XANSYS - THE School of Hard Knocks
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For perfectly incompressible material, Poisson’s ratio of 0.5 is
unacceptable as it makes the bulk modulus infinite. To keep ANSYS
happy, use 0.49995
Polyurethane foams ?? Use Hyper56 with Blatz-Ko function
(Keyopt(2)=1) IF you have the parameters for it. The literature is
leaning towards M-R or hyperelastic w/ Ogden function.
Polyurethane foams and access to LS-DYNA ??
See this reference:
http://web.bham.ac.uk/millsnj/pdf/matpaperkyoto.pdf
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References on the Internet
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All about Testing Hyperelastic Materials and more…
http://www.axelproducts.com/pages/Downloads.html
www.PolymerFEM.com
As the name suggests it is THE place to start w/ questions pertaining
to elastomer modeling.
(mostly ABAQUS but some ANSYS and LS-DYNA models are
readily available).
SILICONE RUBBER TESTING
http://www.pp.bme.hu/me/2001_1/pdf/me2001_1_11.pdf
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Conclusions
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Test the material at hand
Take the Advanced Nonlinearities Class offered by your ASD.
Use these RESOURCES
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IMPACT Engineering Solutions, Inc.
ANSYS Customer Portal – Sample Models
Ansys.net
Axel Products
Datapoint Labs
PolymerFEM.com
XANSYS – Ask (wisely) and thou shall receive…
Wish List : Currently ANSYS does not have the option for Mullins
Effect to account for hysteretic damage. Is this option something
we can expect to see in the near future ???
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©2005 – IMPACT Engineering Solutions, Inc.
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