UHYPER_STRETCH

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

This page discusses:

Elements tested
Problem description
Results and discussion
Input files

Products Abaqus/Standard

Elements tested

C3D8
C3D8RH
CPE4
CPS4
CPS4R

Problem description

This set of verification problems tests the correctness of the results obtained using user subroutine UHYPER_STRETCH for various element types and loading paths. In addition, it tests the variables passed into UHYPER_STRETCH and the usage of the property table in UHYPER_STRETCH.

Each test consists of two coincident elements. Both elements use the same material model and are subject to identical load histories. One of the elements is a reference element with the hyperelastic behavior specified using either a native Abaqus hyperelastic model (neo-Hookean or polynomial [N=2] model) or user subroutine UHYPER. The same material response is specified in the second element using user subroutine UHYPER_STRETCH. Four different sets of material data are used. All the materials and their coefficients are chosen such that they can be expressed in the Valanis-Landel form (see Valanis-Landel Form), which is the required form by user subroutine UHYPER_STRETCH.

Material 1:

Neo-Hookean hyperelastic material.

Table 1. Neo-Hookean material coefficients.
$C_{10}$	$D_{1}$
80.0	2.013423 × 10^-4

Material 2:

Polynomial (N=2) isotropic hyperelastic behavior.

Table 2. Polynomial coefficients.
$C_{10}$	$C_{01}$	$C_{11}$	$C_{20}$	$C_{02}$	$D_{1}$
480.0	-160.0	0.0	80.0	0.0	2.013423 × 10^-4

Material 3:

Polynomial (N=2) isotropic hyperelastic behavior with temperature-dependent coefficients.

Table 3. Temperature-dependent polynomial coefficients.
$C_{10}$	$C_{01}$	$C_{11}$	$C_{20}$	$C_{02}$	$D_{1}$	Temperature
960.0	-320.0	0.0	160.0	0.0	2.013423 × 10^-4	0.0
480.0	-160.0	0.0	80.0	0.0	2.013423 × 10^-4	20.0
240.0	-80.0	0.0	40.0	0.0	2.013423 × 10^-4	40.0

Material 4:

Polynomial (N=2) isotropic hyperelastic behavior with field variable-dependent coefficients.

Table 4. Field variable-dependent polynomial coefficients.
$C_{10}$	$C_{01}$	$C_{11}$	$C_{20}$	$C_{02}$	$D_{1}$	Field variable
960.0	-320.0	0.0	160.0	0.0	2.013423 × 10^-4	0.0
480.0	-160.0	0.0	80.0	0.0	2.013423 × 10^-4	15.0
240.0	-80.0	0.0	40.0	0.0	2.013423 × 10^-4	30.0

Results and discussion

The tests in this section are set up as cases of homogeneous deformation. In each case, the results in the testing elements obtained using user subroutine UHYPER_STRETCH match the results in the reference element obtained using either user subroutine UHYPER or a native Abaqus hyperelastic model.

Input files

uhyper_stretch_c3d8_comp_shear.inp: Neo-Hookean hyperelasticity, compressible, three-dimensional elements, simple shear.
uhyper_stretch_c3d8_comp_tension.inp: Neo-Hookean hyperelasticity, compressible, three-dimensional elements, uniaxial tension.
uhyper_stretch_c3d8rh_comp_fv_tc.inp: Polynomial hyperelasticity with field variable-dependent coefficients, compressible, hybrid elements, property table.
uhyper_stretch_c3d8rh_incomp_temp_tc.inp: Polynomial hyperelasticity with field variable-dependent coefficients, incompressible, hybrid elements, property table.
uhyper_stretch_cpe4_comp_shear.inp: Neo-Hookean hyperelasticity, compressible, simple shear.
uhyper_stretch_cpe4_comp_tension.inp: Neo-Hookean hyperelasticity, compressible, uniaxial tension.
uhyper_stretch_cps4_comp_temp_tc.inp: Polynomial hyperelasticity with temperature-dependent coefficients, compressible, property table.
uhyper_stretch_cps4r_comp_sdv.inp: Polynomial hyperelasticity, compressible, solution-dependent variables, property table.
uhyper_uhyper_stretch.f: User subroutines UHYPER and UHYPER_STRETCH used in uhyper_stretch_c3d8_comp_shear.inp, uhyper_stretch_c3d8_comp_tension.inp, uhyper_stretch_cpe4_comp_shear.inp, and uhyper_stretch_cpe4_comp_tension.inp.
uhyper_stretch_tc.f: User subroutine UHYPER_STRETCH used in uhyper_stretch_c3d8rh_comp_fv_tc.inp, uhyper_stretch_c3d8rh_incomp_temp_tc.inp, uhyper_stretch_cps4_comp_temp_tc.inp, and uhyper_stretch_cps4r_comp_sdv.inp.