Mechanical APDL Structural Analysis Guide

Data outside the experimental strain values are assumed to be constant; therefore, all experimental
data should cover the simulated deformation range as measured by the first deformation invariant
(expressed by Equation 4.196 in the Mechanical APDL Theory Reference).

The following table shows various I 1 values and the corresponding engineering strains in each experi-

mental deformation for an incompressible material:

Example I 1 Values and Corresponding Experimental Strains

I 1 3.01 3.1 4.0 10.0

Uniaxial ten- 0.059 0.193 0.675 2.057

sion

Biaxial tension 0.030 0.098 0.362 1.232

Uniaxial com- -0.057 -0.171 -0.461 -0.799

pression

Planar shear 0.051 0.171 0.618 1.981

For example, a simulation that includes deformation up to I 1 = 10.0 requires experimental data in uni-

axial tension up to about 206 percent engineering strain, biaxial tension to 123 percent, uniaxial com-
pression to -80 percent, and planar shear to 198 percent. The values in the table were obtained by
solving Equation 4.252 for uniaxial tension,Equation 4.261 for biaxial tension,Equation 4.268 for planar
shear (all described in the Mechanical APDL Theory Reference), and converting the biaxial tension strain
to equivalent uniaxial compression strain.

Experimental data that does not include the lateral strain are assumed to be for incompressible mater-
ial behavior; however, this data can be combined with a volumetric potential function to simulate the
behavior of nearly incompressible materials. Combining incompressible experimental data with a volu-
metric model that includes significant compressibility is not restricted, but should be considered carefully
before use in a simulation.

8.4.1.2.11. User-Defined Hyperelastic Option (TB,HYPER,,,,USER)

The User option (TB,HYPER,,,,USER) allows you to use the subroutine USERHYPER to define the derivatives
of the strain energy potential with respect to the strain invariants. Refer to the Guide to User-Programmable
Features for a detailed description on writing a user hyperelasticity subroutine.

8.4.1.3. Bergstrom-Boyce Hyperviscoelastic Material Model

Use the Bergstrom-Boyce material model (TB,BB) for modeling the strain-rate-dependent, hysteretic
behavior of materials that undergo substantial elastic and inelastic strains. Examples of such materials
include elastomers and biological materials. The model assumes an inelastic response only for shear
distortional behavior; the response to volumetric deformations is still purely elastic.

The following example input listing shows a typical use of the Bergstrom-Boyce option:

TB, BB, 1, , , ISO !Activate Bergstrom-Boyce ISO data table

TBDATA, 1, 1.31 !Define material constant μA ,

TBDATA, 2, 9.0 !Define N0=(λAlock)^2

TBDATA, 3, 4.45 !Define material constant μB

TBDATA, 4, 9.0 !Define N1=(λBlock)2

TBDATA, 5, 0.33 !Define material constant

TBDATA, 6, -1 !Define material constant c

TBDATA, 7, 5.21 !Define material constant m

!

TB, BB, 1, , , PVOL !Activate Bergstrom-Boyce PVOL data table

TBDATA, 1, 0.001! as 1/K, K is the bulk modulus

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Nonlinear Structural Analysis