Testing, Modeling and Validation for

Rubber Simulation in ANSYS

Hubert Lobo & Brian Croop

expert material testing | CAE material parameters | CAE Validation | software & infrastructure for materials | materials knowledge | electronic lab notebooks
What Defines a Hyperelastic Material?
• Required behavior
• Recovery of strain
• Not just high elongation
• No yielding
• Poisson’s ratio ~ 0.5

“Hyperelastic” “Ductile Plastic”

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Curve Shape
• Curve Shape
• Increasing stress with strain
• No multiple inflection
• No zero slope point

HDPE

Latex

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In Between Materials
• Elastomers
• Blend of polymer and rubber
• Hyperelastic to some point
• Yielding
• Urethanes
• Polyester elastomers
• Some TPEs

PUR

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Rubber vs Elastomer
• Difference in damage mechanism
• Rubber damage by cross-link breakage
• Stress decrease after damage
• Softer upon reloading
• Returns to initial shape
• Elastomer damage by plasticity
• Irrecoverable strains (becomes larger)
• Stiffer upon reloading

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Considerations Prior to Testing and Modeling
• What Strains do You Expect?
• Material models will be determined by strain range.
• Small strains may lead to simple models
• Environment
• Large temperature effect on behavior
• Cold temperatures lead to plastic behavior
• High temperatures may cause degradation
• Chemicals, oils can change behavior
• Is the Material Damaged Prior to Your Simulation?
• Hyperelastic materials soften after being deformed
• Cross-link chains are broken
• Material should be pre-cycled if interested only in long term behavior
• Initial installation can be simulated using non-cycled data
• Capturing Mullins effect can be incorporated into the material model
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Characterizing Hyperelastic Materials
• Multiple modes of deformation to define material models
• Uniaxial Tension
• Uniaxial Compression
• Planar Shear
• Biaxial Tension
• Volumetric Compression

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Tensile Test

• Uniaxial deformation
• Wide tabs minimize grip
deformation error
• Non-contact extensometry for
precise strain

ASTM Type C
Planar Tension

• Shear deformation
• Large width to length ratio
minimizes contraction in width
direction
• Non-contact extensometry to
eliminate edge effects
• Pneumatic grips used to
prevent slippage
Compressive Test

• Equivalent to biaxial
deformation
• Lubricated platens minimize
“barrelling”
• May contain volumetric effects
• Not good at high strains
Biaxial Tension Test

• Stretch in x & y plane

• Thinning in z-plane
• Suitable for thin specimens
Volumetric Test
• Hydrostatic compression
• Confining fluid provides uniform
hydrostatic pressure
• Needed when hydrostatic stress is
high, eg. Gaskets and seals.

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Biaxial v. Compression Testing

• Equibiaxial and compression data are equivalent

• At least up to moderate strains
300

250

b = (1/(c+1))1/2-1 200

b = c/((1+b)3)
Stress (psi )

150

biaxial measured by cruciform

100
biaxial calculated from compression

50

0
0 0.1 0.2 0.3 0.4 0.5 0.6
strain (mm/mm)

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Mullins Effect Testing

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Model Selection
• Depends on magnitude of deformation
• Small deformation
• Use Neo-Hookean model
• Large deformation
• 0-100% strain typically Mooney-Rivlin
• Over 100% Ogden

know your real life strains before you test

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Typical rubber data

• Things to Note 3

• Order of stiffness
2
• Uniaxial
• Planar 1
• Biaxial

Stress (MPa)
• Continuous slope 0
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2
through origin Uniaxial Tension Data
-1
• No inflections Equibiaxial Tension Data
Planar Shear Data
• Equal number of -2
points per curve
-3
Strain (mm/mm)

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Fitting of Test Data to Material Models
• Most models are strain energy based
• Stretch ratio conversion
• Each mode of deformation produces deformations in the other modes
Deformation Gradient Deformation Mode Conversion
 
1 0 0       1 ,     1
  1 U U 2 3

F  0  2 0 
U

 
0 0
  3 
 
     1 ,  1 
2
1 2 B 3 B
1st and 2nd Invariants
I    
2 2 2
1 1 2 3

I   
2 2 2
2 1 2 3
     1 ,  1 , 
1 S S 2 3
 1
 S

V
       V
3
1 2 3 V
,
V 0

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Fitting of Test Data to Material Models
• Mooney-Rivlin 1st and 2nd Invariants
N N

I    
1
C ( I 1  3) ( I 2  3)  
i j 2i 2 2 2
U ij ( ( J  1) 1 1 2 3
i  j 1 i 1 D
I   
i 2 2 2
2 1 2 3

• Ogden
2
U        3  1 ( J 1)
N
i i i i
N 2i


2 1 2 3
i 1
i D i 1 i

• Take derivative to get into stress

U 1 U U
 Uniaxial

  Biaxial

2   Planar



• Fit simultaneous equations

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Rubber Modeling

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Handling failure
• Perform tear strength test on rubber
• ASTM D624 Type C ‘bow-tie’
• Obtain test data

Credits: Nair, Bestelmeyer, Lobo (2009)

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Handling failure in elastomers
• Model failure with cohesive elements
• Obtain fail strength to elements Coupling definitions

• Apply to real-life model

• Damage path must be known or
postulated
Cohesive Elements

Failure mode during the tear test (ASTM D624 Type C Specimen)

Credits: Nair, Bestelmeyer, Lobo (2009)

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CAETestBench Validation Mechanism
• Use a standardized geometry
• May not be real-life part
• Test must be ‘perfect’
• Boundary conditions can be correctly simulated
• Load case can be correctly simulated
• Comparison
• Obtain test output that is also available in simulation
• For example, DIC strain pattern, force v. time…

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Overview of this Validation
• Measure hyperelastic properties
• Create material model
• Devise “standardized” compression test
• Both faces slipping (closed loop case)
• Top face fixed (open loop)
• Top and bottom faces fixed (open loop)
• Simulate and compare to experiment
• Quantify simulation accuracy

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Mooney-Rivlin 9 Parameter

Matereality Workbench

C10 3.47E-01 MPa C10 3.64E-01 MPa

C01 3.52E-02 MPa C01 -5.81E-03 MPa
C20 -1.36E-01 MPa C20 -1.19E-01 MPa
C11 2.88E-02 MPa C11 4.54E-02 MPa
C02 -7.90E-03 MPa C02 -1.11E-02 MPa
C30 2.33E-02 MPa C30 1.38E-02 MPa
C21 1.44E-02 MPa C21 1.35E-02 MPa
C12 -1.15E-02 MPa C12 -9.47E-03 MPa
C03 1.91E-03 MPa C03 1.56E-03 MPa
D1 1.34E-03 1/MPa C10 3.64E-01 MPa
Ogden 3 Term
Matereality

MU1 3.715023 MPa

MU2 -1.58648 MPa
MU3 -1.58647 MPa
A1 1.141617
A2 0.994652
A3 0.99404
D1 0.001763 1/MPa
D2 3.1128e-5 1/MPa
D3 -1.5446e-6 1/MPa
Simulation B.C.s

• Top is displaced
• Bottom platen fixed
• Contact varies between
sliding and fixed
• Quarter model

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Contact Conditions

Quarter model, symmetry on the x and y faces

Fixed bottom platen

Displacement to 6.35mm on the top platen

Bonded contacts accompany a rough contact for the circumferential

side
Contact Location Type

Slipping Top Frictionless

Bottom Frictionless

Mixed Top Frictionless

Bottom Bonded

Fixed Top Bonded

Bottom Bonded

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Validation Experiments

• Slip
• Mixed
• Fixed

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Slip

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Fixed

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Contact Issues

• Fixed boundary has roll over

which is addressed with the
rough contact
• The corner element and
nearby mesh are distorted

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Mixed

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Mix - Nonlinear Adaptive Mesh

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Results

• Accurate for moderate strains (40%)

• Closed-loop validation unsurprisingly shows least deviation
• The most complex set of boundary conditions (mixed) has the
least accuracy
• Different data fitting programs yields variability on parameters,
with only slight impact on the simulation

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Conclusions

• Validation of simulation quantifies the difference between virtual

world and reality
• Should be performed each time a material is being tested for use
in simulation
• Data, model, and simulation can be checked using test cases
that contain real-life behaviors, giving confidence to the analyst

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