UANISOHYPER_INV and VUANISOHYPER_INV

This problem contains basic test cases for one or more Abaqus elements and features.

The following topics are discussed:

Features tested
Elements tested
Problem description
Results and discussion
Input files

ProductsAbaqus/StandardAbaqus/Explicit

Features tested

Family of user subroutines to define anisotropic hyperelastic material behavior.

Elements tested

C3D8

C3D8H

C3D8R

CPEG4

CPE4H

CPE4R

CPE8R

Problem description

This set of verification problems is primarily intended to test the variables that are passed into UANISOHYPER_INV in Abaqus/Standard or VUANISOHYPER_INV in Abaqus/Explicit. These tests also verify that the derivatives of the strain energy function defined by the user are transferred properly to the solution process. In each test the material properties are specified using the user strain energy potential for the testing elements, for which the strain energy function and the associated derivatives are defined in user subroutines UANISOHYPER_INV and VUANISOHYPER_INV. Each test contains one reference element with material properties specified with anisotropic hyperelasticity, which provides the reference solution. Three different sets of material data are used, as described below.

Material 1

Holzapfel-Gasser-Ogden material with two families of fibers:

Holzapfel-Gasser-Ogden coefficients:
$C_{10}$ = 7.64., $k_{1}$ = 996.6, $k_{2}$ = 524.6, $κ$ = 0.226.
Fiber directions (N=2):
	$A_{1} = (\cos γ, \sin γ, 0),$
	$A_{2} = (\cos γ, - \sin γ, 0),$
with $γ = {49.98}^{o} .$
Compressible case: $D = 10^{- 8}$

Material 2

Polynomial (N=2) isotropic hyperelastic behavior

Polynomial coefficients (N=2):
	$C_{10}$ = 100.0
	$C_{01}$ = 50.0
	$C_{20}$ = 10.0
	$C_{11}$ = 20.0
	$C_{02}$ = 30.0
Compressible case: $D_{1}$ = 0.01, $D_{2}$ =0.0

Material 3

Generalized Fung energy function implemented in terms of pseudo invariants. Two implementations are considered: one with the components of the modified Green strain expressed in terms of ${\bar{I}}_{4 (α β)}$ type invariants, and the other in terms of ${\bar{I}}_{4 (α β)}$ and ${\bar{I}}_{5 (α β)}$ type invariants.

Fung coefficients:
	$c = 26.95 \times 10^{3}$
	$b_{1111}$ = 0.9925
	$b_{1122}$ = 0.0749
	$b_{2222}$ = 0.4180
	$b_{1133}$ = 0.0295
	$b_{2233}$ = 0.0193
	$b_{3333}$ = 0.0089
	$b_{1212}$ = 5.0
	$b_{1313}$ = 5.0
	$b_{2323}$ = 5.0
Compressible case: $D$ = 0.1

Results and discussion

The tests in this section are set up as cases of homogeneous deformation of a single element of unit dimensions. Consequently, the results are identical for all integration points within the element. In each case the results in the testing elements match the solution in the reference element.

Input files

Abaqus/Standard input files

uaniso_inv_hgople.inp: Holzapfel-Gasser-Ogden anisotropic hyperelasticity, compressible, uniaxial plane strain tension.
uaniso_inv_isople.inp: Polynomial hyperelasticity, incompressible, uniaxial plane strain tension, hybrid elements.
uaniso_inv_fung.inp: Fung anisotropic hyperelasticity, compressible, uniaxial plane strain tension.
uanisohyper_inv.f: User subroutine UANISOHYPER_INV used in the above tests.

Abaqus/Explicit input files

vuaniso_inv_hgople.inp: Holzapfel-Gasser-Ogden anisotropic hyperelasticity, compressible, uniaxial plane strain tension.
vuaniso_inv_isople.inp: Polynomial hyperelasticity, compressible, uniaxial plane strain tension, hybrid elements.
vuaniso_inv_fung.inp: Fung anisotropic hyperelasticity, compressible, uniaxial plane strain tension.
vuanisohyper_inv.f: User subroutine VUANISOHYPER_INV used in the above tests.