Elastic materials

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

This page discusses:

Linear orthotropic elastic materials
Linear anisotropic elastic material
Logarithmic porous elasticity
Power law–based porous elasticity
Hypoelasticity
Hyperelasticity with polynomial strain energy function
Hyperelasticity with reduced polynomial strain energy function
Hyperelasticity with neo-Hookean strain energy function
Hyperelasticity with Mooney-Rivlin strain energy function
Hyperelasticity with Yeoh strain energy function
Hyperelasticity with Ogden strain energy function
Hyperelasticity with Arruda-Boyce strain energy function
Hyperelasticity with Van der Waals strain energy function
Hyperelasticity with Marlow strain energy function
Hyperfoam
Low-density foam
Anisotropic hyperelasticity with generalized Fung strain energy function
Anisotropic hyperelasticity with Holzapfel strain energy function
No compression
No tension
Compression factor with traction elastic behavior

ProductsAbaqus/StandardAbaqus/Explicit

Linear orthotropic elastic materials

Elements tested

C3D8

CPE4

CPS4

Problem description

Material:


Engineering constants		Stiffness coefficients
$E_{1}$	1000.	$D_{1111}$	1000.
$E_{2}$	1000.	$D_{1122}$	0.
$E_{3}$	1000.	$D_{2222}$	1010.1
$ν_{12}$	0.	$D_{1133}$	0.
$ν_{13}$	0.	$D_{2233}$	101.01
$ν_{23}$	0.1	$D_{3333}$	1010.1
$G_{12}$	100.	$D_{1212}$	100.
$G_{13}$	100.	$D_{1313}$	100.
$G_{23}$	100.	$D_{2323}$	100.

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

meloro3ltr.inp: ELASTIC, TYPE=ORTHOTROPIC; C3D8 elements.
meloro2ltr.inp: ELASTIC, TYPE=ORTHOTROPIC; CPS4 elements.
meleco3ltr.inp: ELASTIC, TYPE=ENGINEERING CONSTANTS; CPE4 elements.

Linear anisotropic elastic material

Elements tested

C3D8

Problem description

Material:


Stiffness coefficients
$D_{1111}$	2.24e11
$D_{1122}$	4.79e5
$D_{2222}$	1.23e11
$D_{1133}$	4.21e5
$D_{2233}$	4.74e5
$D_{3333}$	1.21e11
$D_{1112}$	1.e6
$D_{2212}$	2.e6
$D_{3312}$	3.e6
$D_{1212}$	7.69e10
$D_{1113}$	4.e6
$D_{2213}$	5.e6
$D_{3313}$	6.e6
$D_{1213}$	7.e6
$D_{1313}$	7.69e10
$D_{1123}$	8.e6
$D_{2223}$	9.e6
$D_{3323}$	10.e6
$D_{1223}$	11.e6
$D_{1323}$	12.e6
$D_{2323}$	9.e9

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

melano3ltr.inp: ELASTIC, TYPE=ANISOTROPIC; C3D8 elements.

Logarithmic porous elasticity

Elements tested

CAX8R

Problem description

Material:


Logarithmic bulk modulus, $κ$ = 1.0
Poisson's ratio, $ν$ = 0.3

(The units are not important.)

Initial conditions


Initial void ratio, $e_{0}$ = 1.08

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

mpespo3ahc.inp: Hydrostatic compression, CAX8R elements.
mpespo3vlp.inp: Linear perturbation steps containing LOAD CASE, hydrostatic compression, CAX8R elements.

Power law–based porous elasticity

Elements tested

C3D8, C3D8R

Problem description

Material:


$E_{r e f}$ = 5000.0
$p_{r e f}$ = 3.0
$p_{0}$ = 1.0
$n$ = 0.5
$ν_{\infty}$ = 0.3
$ν_{0}$ = 0.3
$m$ = 1.0

(The units are not important.)

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

porelapowlawtests.inp: Hydrostatic compression, C3D8 and C3D8R elements.

Hypoelasticity

Elements tested

CPS4R

Problem description

Material:

The following dependence of E on the second strain invariant $I_{2}$ is used:


E	$ν$	$I_{2}$
637.5	0.499	4.5420e−3
700.3	0.499	1.6621e−2
765.7	0.499	3.4418e−2
840.7	0.499	5.6607e−2
917.4	0.499	8.2201e−2

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

mhooto2hut.inp: Nearly incompressible, uniaxial tension, CPS4R elements.

Hyperelasticity with polynomial strain energy function

Elements tested

C3D8RH

CAX8

CGAX8H

CPS4R

Problem description

Material:


Polynomial coefficients (N=1): $C_{10}$ = 80., $C_{01}$ = 20.
Compressible case: $D_{1}$ = 0.001.
Test data (N=2): Treloar's experimental data.

(The units are not important.)

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

Coefficient input

mhecoo3hut.inp: Incompressible, uniaxial tension, C3D8RH elements.
mhecoo3ibt.inp: Incompressible, biaxial tension, C3D8RH elements.
mhecoo3gsh.inp: Incompressible, planar tension, C3D8RH elements.
mhecoo3vlp.inp: Incompressible, uniaxial tension with static linear perturbation steps containing LOAD CASE, C3D8RH elements.
mhecot3hut.inp: Incompressible, temperature-dependent, uniaxial tension, C3D8RH elements.

mhecdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhecdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhecdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhecdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

mhecoo2hut.inp: Incompressible, uniaxial tension, CPS4R elements.
mhecoo2ibt.inp: Incompressible, biaxial tension, CPS4R elements.
mhecoo2gsh.inp: Incompressible, planar tension, CPS4R elements.

mhecdo2hut.inp: Compressible, uniaxial tension, CPS4R elements.
mhecdo2ibt.inp: Compressible, biaxial tension, CPS4R elements.
mhecdo2gsh.inp: Compressible, planar tension, CPS4R elements.

mhecoo2spt.inp: Incompressible, pure torsion, CGAX8H elements.
mhecoo2eit.inp: Incompressible; extension, inflation, and torsion; CGAX8H elements.
mhecoo2eis.inp: Incompressible; extension, inflation, and shear; CAX8 elements.

Test data input

mhetdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhetdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhetdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhetdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.
mhetdi3ahc.inp: Compressible, volumetric compression with initial stresses, C3D8RH elements.

Hyperelasticity with reduced polynomial strain energy function

Elements tested

C3D8RH

CPS4R

Problem description

Material:


Polynomial coefficients (N=1): $C_{10}$ = 100.
Compressible case: $D_{1}$ = 0.001.
Test data (N=6): Treloar's experimental data.

(The units are not important.)

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

Coefficient input

mhrcoo3hut.inp: Incompressible, uniaxial tension, C3D8RH elements.
mhrcoo3ibt.inp: Incompressible, biaxial tension, C3D8RH elements.
mhrcoo3gsh.inp: Incompressible, planar tension, C3D8RH elements.
mhrcoo3vlp.inp: Incompressible, uniaxial tension with static linear perturbation steps containing LOAD CASE, C3D8RH elements.
mhrcot3hut.inp: Incompressible, temperature-dependent, uniaxial tension, C3D8RH elements.

mhrcdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhrcdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhrcdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhrcdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

mhrcoo2hut.inp: Incompressible, uniaxial tension, CPS4R elements.
mhrcoo2ibt.inp: Incompressible, biaxial tension, CPS4R elements.
mhrcoo2gsh.inp: Incompressible, planar tension, CPS4R elements.

mhrcdo2hut.inp: Compressible, uniaxial tension, CPS4R elements.
mhrcdo2ibt.inp: Compressible, biaxial tension, CPS4R elements.
mhrcdo2gsh.inp: Compressible, blanar tension, CPS4R elements.

Test data input

mhrtdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhrtdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhrtdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhrtdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

Hyperelasticity with neo-Hookean strain energy function

Elements tested

C3D8RH

CPS4R

Problem description

Material:


Neo-Hookean coefficient: $C_{10}$ = 100.
Compressible case: $D_{1}$ = 0.001.
Test data: Treloar's experimental data.

(The units are not important.)

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

Coefficient input

mhncoo3hut.inp: Incompressible, uniaxial tension, C3D8RH elements.
mhncoo3ibt.inp: Incompressible, biaxial tension, C3D8RH elements.
mhncoo3gsh.inp: Incompressible, planar tension, C3D8RH elements.
mhncoo3vlp.inp: Incompressible, uniaxial tension with static linear perturbation steps containing LOAD CASE, C3D8RH elements.
mhncot3hut.inp: Incompressible, temperature-dependent, uniaxial tension, C3D8RH elements.

mhncdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhncdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhncdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhncdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

mhncoo2hut.inp: Incompressible, uniaxial tension, CPS4R elements.
mhncoo2ibt.inp: Incompressible, biaxial tension, CPS4R elements.
mhncoo2gsh.inp: Incompressible, planar tension, CPS4R elements.

mhncdo2hut.inp: Compressible, uniaxial tension, CPS4R elements.
mhncdo2ibt.inp: Compressible, biaxial tension, CPS4R elements.
mhncdo2gsh.inp: Compressible, planar tension, CPS4R elements.

Test data input

mhntdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhntdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhntdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhntdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

Hyperelasticity with Mooney-Rivlin strain energy function

Elements tested

C3D8RH

CPS4R

Problem description

Material:


Mooney-Rivlin coefficients: $C_{10}$ = 80., $C_{01}$ = 20.
Compressible case: $D_{1}$ = 0.001.
Test data: Treloar's experimental data.

(The units are not important.)

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

Coefficient input

mhmcoo3hut.inp: Incompressible, uniaxial tension, C3D8RH elements.
mhmcoo3ibt.inp: Incompressible, biaxial tension, C3D8RH elements.
mhmcoo3gsh.inp: Incompressible, planar tension, C3D8RH elements.
mhmcoo3vlp.inp: Incompressible, uniaxial tension with static linear perturbation steps containing LOAD CASE, C3D8RH elements.
mhmcot3hut.inp: Incompressible, temperature-dependent, uniaxial tension, C3D8RH elements.

mhmcdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhmcdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhmcdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhmcdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

mhmcoo2hut.inp: Incompressible, uniaxial tension, CPS4R elements.
mhmcoo2ibt.inp: Incompressible, biaxial tension, CPS4R elements.
mhmcoo2gsh.inp: Incompressible, planar tension, CPS4R elements.

mhmcdo2hut.inp: Compressible, uniaxial tension, CPS4R elements.
mhmcdo2ibt.inp: Compressible, biaxial tension, CPS4R elements.
mhmcdo2gsh.inp: Compressible, planar tension, CPS4R elements.

Test data input

mhmtdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhmtdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhmtdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhmtdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

Hyperelasticity with Yeoh strain energy function

Elements tested

C3D8RH

CPS4R

Problem description

Material:


Yeoh coefficients: $C_{10}$ = 100., $C_{20}$ = −1., $C_{30}$ = 0.01.
Compressible case: $D_{1}$ = 0.001.
Test data: Treloar's experimental data.

(The units are not important.)

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

Coefficient input

mhycoo3hut.inp: Incompressible, uniaxial tension, C3D8RH elements.
mhycoo3ibt.inp: Incompressible, biaxial tension, C3D8RH elements.
mhycoo3gsh.inp: Incompressible, planar tension, C3D8RH elements.
mhycoo3vlp.inp: Incompressible, uniaxial tension with static linear perturbation steps containing LOAD CASE, C3D8RH elements.
mhycot3hut.inp: Incompressible, temperature-dependent, uniaxial tension, C3D8RH elements.

mhycdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhycdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhycdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhycdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

mhycoo2hut.inp: Incompressible, uniaxial tension, CPS4R elements.
mhycoo2ibt.inp: Incompressible, biaxial tension, CPS4R elements.
mhycoo2gsh.inp: Incompressible, planar tension, CPS4R elements.

mhycdo2hut.inp: Compressible, uniaxial tension, CPS4R elements.
mhycdo2ibt.inp: Compressible, biaxial tension, CPS4R elements.
mhycdo2gsh.inp: Compressible, planar tension, CPS4R elements.

Test data input

mhytdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhytdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhytdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhytdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

Hyperelasticity with Ogden strain energy function

Elements tested

C3D8RH

CAX8

CGAX8H

CPS4R

Problem description

Material:


Ogden coefficients (N=2): $μ_{1}$ = 160., $α_{1}$ = 2., $μ_{2}$ = 40., $α_{2}$ = −2.
Compressible case: $D_{1}$ = 0.001.
Test data (N=2): Treloar's experimental data.

(The units are not important.)

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

Coefficient input

mhgcoo3hut.inp: Incompressible, uniaxial tension, C3D8RH elements.
mhgcoo3ibt.inp: Incompressible, biaxial tension, C3D8RH elements.
mhgcoo3gsh.inp: Incompressible, planar tension, C3D8RH elements.
mhgcoo3vlp.inp: Incompressible, uniaxial tension with static linear perturbation steps containing LOAD CASE, C3D8RH elements.
mhgcot3hut.inp: Incompressible, temperature-dependent, uniaxial tension, C3D8RH elements.

mhgcdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhgcdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhgcdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhgcdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

mhgcoo2hut.inp: Incompressible, uniaxial tension, CPS4R elements.
mhgcoo2ibt.inp: Incompressible, biaxial tension, CPS4R elements.
mhgcoo2gsh.inp: Incompressible, planar tension, CPS4R elements.

mhgcdo2hut.inp: Compressible, uniaxial tension, CPS4R elements.
mhgcdo2ibt.inp: Compressible, biaxial tension, CPS4R elements.
mhgcdo2gsh.inp: Compressible, planar tension, CPS4R elements.

mhgcoo2spt.inp: Incompressible, pure torsion, CGAX8H elements.
mhgcoo2eit.inp: Incompressible; extension, inflation, and torsion; CGAX8H elements.
mhgcoo2eis.inp: Incompressible; extension, inflation, and shear; CAX8 elements.

Test data input

mhgtdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhgtdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhgtdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhgtdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

Hyperelasticity with Arruda-Boyce strain energy function

Elements tested

C3D8RH

CPS4R

Problem description

Material:


Arruda-Boyce coefficients: $μ$ = 200., $λ_{m}$ = 5.
Compressible case: $D_{1}$ = 0.001.
Test data: Treloar's experimental data.

(The units are not important.)

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

Coefficient input

mhacoo3hut.inp: Incompressible, uniaxial tension, C3D8RH elements.
mhacoo3ibt.inp: Incompressible, biaxial tension, C3D8RH elements.
mhacoo3gsh.inp: Incompressible, planar tension, C3D8RH elements.
mhacoo3vlp.inp: Incompressible, uniaxial tension with static linear perturbation steps containing LOAD CASE, C3D8RH elements.
mhacot3hut.inp: Incompressible, temperature-dependent, uniaxial tension, C3D8RH elements.

mhacdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhacdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhacdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhacdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

mhacoo2hut.inp: Incompressible, uniaxial tension, CPS4R elements.
mhacoo2ibt.inp: Incompressible, biaxial tension, CPS4R elements.
mhacoo2gsh.inp: Incompressible, planar tension, CPS4R elements.

mhacdo2hut.inp: Compressible, uniaxial tension, CPS4R elements.
mhacdo2ibt.inp: Compressible, biaxial tension, CPS4R elements.
mhacdo2gsh.inp: Compressible, planar tension, CPS4R elements.

Test data input

mhatdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhatdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhatdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhatdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

Hyperelasticity with Van der Waals strain energy function

Elements tested

C3D8RH

CPS4R

Problem description

Material:


Van der Waals coefficients: $μ$ = 200., $λ_{m}$ = 10., a = 0.1, $β$ = 0.
Compressible case: $D_{1}$ = 0.001.
Test data: Treloar's experimental data.
Test data (parameter $β$ held constant): Treloar's experimental data, $β$ = 0.

(The units are not important.)

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

Coefficient input

mhvcoo3hut.inp: Incompressible, uniaxial tension, C3D8RH elements.
mhvcoo3ibt.inp: Incompressible, biaxial tension, C3D8RH elements.
mhvcoo3gsh.inp: Incompressible, planar tension, C3D8RH elements.
mhvcoo3vlp.inp: Incompressible, uniaxial tension with static linear perturbation steps containing LOAD CASE, C3D8RH elements.
mhvcot3hut.inp: Incompressible, temperature-dependent, uniaxial tension, C3D8RH elements.

mhvcdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhvcdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhvcdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhvcdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

mhvcoo2hut.inp: Incompressible, uniaxial tension, CPS4R elements.
mhvcoo2ibt.inp: Incompressible, biaxial tension, CPS4R elements.
mhvcoo2gsh.inp: Incompressible, planar tension, CPS4R elements.

mhvcdo2hut.inp: Compressible, uniaxial tension, CPS4R elements.
mhvcdo2ibt.inp: Compressible, biaxial tension, CPS4R elements.
mhvcdo2gsh.inp: Compressible, planar tension, CPS4R elements.

Test data input

mhvtdo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhvtdo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhvtdo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhvtdo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

Test data input (parameter β held constant)

mhvtbo3hut.inp: Compressible, uniaxial tension, C3D8RH elements.
mhvtbo3ibt.inp: Compressible, biaxial tension, C3D8RH elements.
mhvtbo3gsh.inp: Compressible, planar tension, C3D8RH elements.
mhvtbo3ahc.inp: Compressible, volumetric compression, C3D8RH elements.

Hyperelasticity with Marlow strain energy function

Elements tested

C3D8H
C3D8R
CPE4RH
CPE4R
CPS4R
S4R
SC8R
M3D4R

T2D2
T3D2
B21
B22
B31
B32
B31OS
B32OS

PIPE21
PIPE22
PIPE31
PIPE32

Problem description

The tests in this section verify that the results generated using the Marlow hyperelastic model with different elements agree with the test data specified in the model.

Results and discussion

The results agree well with the test data specified for the Marlow model.

Input files

Abaqus/Standard input files

marlow_uniaxial_icmp.inp: Incompressible, C3D8H element, uniaxial tension test data.
marlow_uniaxial_cmp.inp: Compressible, C3D8H element, uniaxial tension and volumetric compression test data.
marlow_uniaxial_pos.inp: Compressible, C3D8H element, uniaxial tension test data, with Poisson's ratio equal to 0.47.
marlow_uniaxial_e3.inp: Compressible, C3D8H element, uniaxial tension test data, with lateral nominal strains specified.
marlow_biaxial_icmp.inp: Incompressible, C3D8H element, uniaxial tension test data.
marlow_biaxial_cmp.inp: Compressible, C3D8H element, biaxial tension and volumetric compression test data.
marlow_biaxial_pos.inp: Compressible, C3D8H element, biaxial tension test data, with Poisson's ratio equal to 0.47.
marlow_biaxial_eb.inp: Compressible, C3D8H element, biaxial tension test data, with lateral nominal strains specified.
marlow_planar_icmp.inp: Incompressible, C3D8H element, planar tension test data.
marlow_planar_cmp.inp: Compressible, C3D8H element, planar tension and volumetric compression test data.
marlow_planar_pos.inp: Compressible, C3D8H element, planar tension test data, with Poisson's ratio equal to 0.47.
marlow_planar_e3.inp: Compressible, C3D8H element, planar tension test data, with lateral nominal strains specified.
marlow_cpe4rh_icmp.inp: Incompressible, CPE4RH element, uniaxial tension test data.
marlow_cpe4rh_cmp.inp: Compressible, CPE4RH element, uniaxial tension and volumetric compression test data.
marlow_cps4r_icmp.inp: Incompressible, CPS4R element, uniaxial tension test data.
marlow_cps4r_cmp.inp: Compressible, CPS4R element, uniaxial tension and volumetric compression test data.
marlow_s4r_icmp.inp: Incompressible, S4R element, uniaxial tension test data.
marlow_s4r_cmp.inp: Compressible, S4R element, uniaxial tension and volumetric compression test data.
marlow_sc8r_cmp.inp: Compressible, SC8R element, uniaxial tension and volumetric compression test data.
marlow_m3d4r_icmp.inp: Incompressible, M3D4R element, uniaxial tension test data.
marlow_m3d4r_cmp.inp: Compressible, M3D4R element, uniaxial tension and volumetric compression test data.
marlow_t2d2_icmp.inp: Incompressible, T2D2 element, uniaxial tension test data.
marlow_t2d2_cmp.inp: Compressible, T2D2 element, uniaxial tension and volumetric compression test data.
marlow_t3d2_icmp.inp: Incompressible, T3D2 element, uniaxial tension test data.
marlow_t3d2_cmp.inp: Compressible, T3D2 element, uniaxial tension and volumetric compression test data.
marlow_b21_icmp.inp: Incompressible, B21 element, uniaxial tension test data.
marlow_b21_cmp.inp: Compressible, B21 element, uniaxial tension and volumetric compression test data.
marlow_b22_icmp.inp: Incompressible, B22 element, uniaxial tension test data.
marlow_b22_cmp.inp: Compressible, B22 element, uniaxial tension and volumetric compression test data.
marlow_b31_icmp.inp: Incompressible, B31 element, uniaxial tension test data.
marlow_b31_cmp.inp: Compressible, B31 element, uniaxial tension and volumetric compression test data.
marlow_b32_icmp.inp: Incompressible, B32 element, uniaxial tension test data.
marlow_b32_cmp.inp: Compressible, B32 element, uniaxial tension and volumetric compression test data.
marlow_b31os_icmp.inp: Incompressible, B31OS element, uniaxial tension test data.
marlow_b31os_cmp.inp: Compressible, B31OS element, uniaxial tension and volumetric compression test data.
marlow_b32os_icmp.inp: Incompressible, B32OS element, uniaxial tension test data.
marlow_b32os_cmp.inp: Compressible, B32OS element, uniaxial tension and volumetric compression test data.
marlow_pipe21_icmp.inp: Incompressible, PIPE21 element, uniaxial tension test data.
marlow_pipe21_cmp.inp: Compressible, PIPE21 element, uniaxial tension and volumetric compression test data.
marlow_pipe22_icmp.inp: Incompressible, PIPE22 element, uniaxial tension test data.
marlow_pipe22_cmp.inp: Compressible, PIPE22 element, uniaxial tension and volumetric compression test data.
marlow_pipe31_icmp.inp: Incompressible, PIPE31 element, uniaxial tension test data.
marlow_pipe31_cmp.inp: Compressible, PIPE31 element, uniaxial tension and volumetric compression test data.
marlow_pipe32_icmp.inp: Incompressible, PIPE32 element, uniaxial tension test data.
marlow_pipe32_cmp.inp: Compressible, PIPE32 element, uniaxial tension and volumetric compression test data.
marlow_combined_ct.inp: Incompressible, T2D2 element, uniaxial tension and compression test data.
marlow_rebar.inp: Incompressible, S4R element, uniaxial tension test data.
marlow_depend.inp: Incompressible, C3D8H element, uniaxial tension test data with field dependencies.
marlow_hysteresis.inp: Incompressible, C3D8H element, uniaxial tension test data, hysteresis analysis.
marlow_initialstress.inp: Compressible, C3D8H element, uniaxial tension test data, with initial stress specified.
marlow_map0.inp: Incompressible, C3D8H element, uniaxial tension test data, needed for the following map solution analysis.
marlow_map.inp: Incompressible, C3D8H element, uniaxial tension test data, map solution analysis.
marlow_visco_c3d8h_icmp.inp: Compressible, C3D8H element, uniaxial tension and relaxation test data.
marlow_visco_c3d8h_cmp.inp: Compressible; C3D8H element; uniaxial tension, volumetric compression, and relaxation test data.
marlow_visco_cps4r_icmp.inp: Compressible, CPS4R element, uniaxial tension and relaxation test data.
marlow_visco_cps4r_cmp.inp: Compressible; CPS4R element; uniaxial tension, volumetric compression, and relaxation test data.
marlow_visco_t3d2_icmp.inp: Compressible, T3D2 element, uniaxial tension and relaxation test data.
marlow_visco_t3d2_cmp.inp: Compressible; T3D2 element; uniaxial tension, volumetric compression, and relaxation test data.
marlow_visco_b21_icmp.inp: Compressible, B21 element, uniaxial tension and relaxation test data.
marlow_visco_b21_cmp.inp: Compressible; B21 element; uniaxial tension, volumetric compression, and relaxation test data.
marlow_visco_b31_icmp.inp: Compressible, B31 element, uniaxial tension and relaxation test data.
marlow_visco_b31_cmp.inp: Compressible; B32 element; uniaxial tension, volumetric compression, and relaxation test data.
marlow_visco_pipe21_icmp.inp: Compressible, PIPE21 element, uniaxial tension and relaxation test data.
marlow_visco_pipe21_cmp.inp: Compressible; PIPE21 element; uniaxial tension, volumetric compression, and relaxation test data.
marlow_visco_pipe31_icmp.inp: Compressible, PIPE31 element, uniaxial tension and relaxation test data.
marlow_visco_pipe31_cmp.inp: Compressible; PIPE31 element; uniaxial tension, volumetric compression, and relaxation test data.
marlow_volumecomp.inp: Volumetric test; C3D8R element; uniaxial tension and volumetric compression.
marlow_sx_s_c3d8r.inp: Base problem for carrying out import from Abaqus/Standard to Abaqus/Explicit, C3D8R element.
marlow_xs_s_c3d8r.inp: Import into Abaqus/Standard from marlow_sx_x_c3d8r.inp.
marlow_sx_s_cpe4r.inp: Base problem for carrying out import from Abaqus/Standard to Abaqus/Explicit, CPE4R element.
marlow_xs_s_cpe4r.inp: Import into Abaqus/Standard from marlow_sx_x_cpe4r.inp.
marlow_sx_s_cps4r.inp: Base problem for carrying out import from Abaqus/Standard to Abaqus/Explicit, CPS4R element.
marlow_xs_s_cps4r.inp: Import into Abaqus/Standard from marlow_sx_x_cps4r.inp.
marlow_sx_s_sc8r.inp: Base problem for carrying out import from Abaqus/Standard to Abaqus/Explicit, SC8R element.
marlow_xs_s_sc8r.inp: Import into Abaqus/Standard from marlow_sx_x_sc8r.inp.
marlow_sx_s_t2d2.inp: Base problem for carrying out import from Abaqus/Standard to Abaqus/Explicit, T2D2 element.
marlow_xs_s_t2d2.inp: Import into Abaqus/Standard from marlow_sx_x_t2d2.inp.

Abaqus/Explicit input files

marlow_xpl_disp.inp: Uniaxial test; displacement control; C3D8R, CPE4R, CPS4R, M3D4R, S4R, and T3D2 elements.
marlow_xpl_load.inp: Uniaxial test; load control; C3D8R, CPE4R, CPS4R, M3D4R, S4R, and T3D2 elements.
marlow_xpl_initstress.inp: Specified initial stress; C3D8R, CPE4R, CPS4R, M3D4R, S4R, and T3D2 elements.
marlow_xpl_mullins.inp: Combination with MULLINS EFFECT; cyclic test; C3D8R, CPE4R, CPS4R, M3D4R, S4R, and T3D2 elements.
marlow_xpl_visco.inp: Creep test; C3D8R, CPE4R, CPS4R, M3D4R, S4R, and T3D2 elements.
marlow_sx_x_c3d8r.inp: Explicit dynamic continuation of marlow_sx_s_c3d8r.inp.
marlow_sx_x_cpe4r.inp: Explicit dynamic continuation of marlow_sx_s_cpe4r.inp.
marlow_sx_x_cps4r.inp: Explicit dynamic continuation of marlow_sx_s_cps4r.inp.
marlow_sx_x_sc8r.inp: Explicit dynamic continuation of marlow_sx_s_sc8r.inp.
marlow_sx_x_t2d2.inp: Explicit dynamic continuation of marlow_sx_s_t2d2.inp.

Hyperfoam

Elements tested

C3D8R

CPS4R

Problem description

Material:


Hyperfoam coefficients (N=3, from fit of test data):
$μ_{1}$ = −48.3291, $α_{1}$ = 3.58961, $μ_{2}$ = 26.3505, $α_{2}$ = 3.84360, $μ_{3}$ = 22.1809, $α_{3}$ = 3.34171.
Test data (N=3): Uniaxial compression, simple shear test data.

An effective Poisson's ratio of $ν_{i}$ = 0 is used, except for $ν_{i}$ = 0.10 for the biaxial test cases and varying $ν_{i}$ in the temperature-dependent case.

(The units are not important.)

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

Coefficient input

mhfcdo2euc.inp: $ν_{i}$ = 0., uniaxial compression, CPS4R elements.
mhfcdo2fbc.inp: $ν_{i}$ = 0.1, biaxial compression, CPS4R elements.
mhfcdo2gsh.inp: $ν_{i}$ = 0., simple shear, CPS4R elements.
mhfcdo3vlp.inp: $ν_{i}$ = 0., uniaxial compression with linear perturbation steps containing LOAD CASE, C3D8R elements.

Test data input

mhftdo3euc.inp: $ν_{i}$ = 0., uniaxial compression, C3D8R elements.
mhftdo3fbc.inp: $ν_{i}$ = 0.1, biaxial compression, C3D8R elements.
mhftdo3gsh.inp: $ν_{i}$ = 0., simple shear, C3D8R elements.
mhftdo3ahc.inp: $ν_{i}$ = 0., volumetric compression, C3D8R elements.
mhfcdt3euc.inp: $ν_{i}$ = 0. − 0.06, temperature-dependent, uniaxial compression, C3D8R elements.
mhftdi3ahc.inp: $ν_{i}$ = 0., volumetric compression with initial stresses, C3D8R elements.

Low-density foam

Elements tested

C3D8R

CPE4R

T3D2

Problem description

The tests in this section verify that the results generated using the low-density foam model with different elements agree with the test data specified in the model.

Results and discussion

The results agree well with the rate-dependent test data specified for the low-density foam model.

Input files

Low density foam with zero Poisson's ratio

lowdensfoam_uni.inp: Uniaxial compression with varying deformation rates; C3D8R, CPE4R, and T3D2 elements.
lowdensfoam_shr.inp: Simple shear test; C3D8R and CPE4R elements.
lowdensfoam_inistress.inp: Specified initial stress; C3D8R, CPE4R, and T3D2 elements.
xx_x1_lowdensfoam.inp: Base problem for carrying out import from Abaqus/Explicit to Abaqus/Explicit. Uniaxial cyclic test; displacement control; C3D8R, CPE4R, and T3D2 elements.
xx_x2_lowdensfoam_n_y.inp: Continuation of xx_x1_lowdensfoam.inp with state imported.

Low density foam with Poisson effects

lowdensfoam_poisson_uni.inp: Uniaxial compression with varying deformation rates; C3D8R and CPE4R elements.
lowdensfoam_poisson_shr.inp: Simple shear test; C3D8R and CPE4R elements.
lowdensfoam_poisson_inistress.inp: Specified initial stress; C3D8R and CPE4R elements.
xx_x1_lowdensfoam_poisson.inp: Base problem for carrying out import from Abaqus/Explicit to Abaqus/Explicit. Uniaxial cyclic test; displacement control; C3D8R and CPE4R elements.
xx_x2_lowdensfoam_poisson_n_y.inp: Continuation of xx_x1_lowdensfoam_poisson.inp with state imported.

Anisotropic hyperelasticity with generalized Fung strain energy function

Elements tested

C3D8
C3D8R
CPE4R
CPS4R
S4R
M3D4R

Problem description

Material:


Fung coefficients
$c$	26.95e3
$b_{1111}$	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
$D$ =1.5e-7 or $D$ =1.0e-8

(The units are not important.)

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

Abaqus/Standard input files

uaniso_inv_fung.inp: Uniaxial tension; built-in Fung orthotropic model verified through user subroutines UANISOHYPER_INV and UANISOHYPER_STRAIN; load control; C3D8 element.
uanisohyper_inv.f: User subroutines UANISOHYPER_INV and UANISOHYPER_STRAIN to define the Fung orthotropic model.
funganiso_mullins_ve.inp: Uniaxial tension, loading-unloading; Fung anisotropic model with Mullins effect and viscoelasticity; C3D8R, CPE4R, and CPS4R elements.

Abaqus/Explicit input files

fung_disp_xpl.inp: Uniaxial cyclic test; displacement control; C3D8R, CPE4R, CPS4R, M3D4R, and S4R elements.
fung_load_xpl.inp: Uniaxial cyclic test; load control; C3D8R, CPE4R, CPS4R, M3D4R, and S4R elements.
fung_visco_xpl.inp: Combination with viscoelastic and Mullins effect; uniaxial cyclic test; C3D8R, CPE4R, CPS4R, M3D4R, and S4R elements.
xx_x1_fung_disp.inp: Base problem for carrying out import from Abaqus/Explicit to Abaqus/Explicit. Uniaxial cyclic test; displacement control; C3D8R, CPE4R, CPS4R, M3D4R, and S4R elements.
xx_x2_fung_disp_n_y.inp: Continuation of xx_x1_fung_disp.inp with state imported.
xx_x1_fung_load.inp: Base problem for carrying out import from Abaqus/Explicit to Abaqus/Explicit. Uniaxial cyclic test; load control; C3D8R, CPE4R, CPS4R, M3D4R, and S4R elements.
xx_x2_fung_load_n_y.inp: Continuation of xx_x1_fung_load.inp with state imported.
xx_x1_fung_visco.inp: Base problem for carrying out import from Abaqus/Explicit to Abaqus/Explicit. Combination with viscoelastic and Mullins effect; uniaxial cyclic test; C3D8R, CPE4R, CPS4R, M3D4R, and S4R elements.
xx_x2_fung_visco_n_y.inp: Continuation of xx_x1_fung_visco.inp with state imported.

Anisotropic hyperelasticity with Holzapfel strain energy function

Elements tested

C3D8R
CPE4R
CPS4R
S4R
M3D4R
C3D10
C3D10HS

Problem description

Material:


Holzapfel 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°.
Compressible case: $D$ = 1.e-6.

(The units are not important.)

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

Abaqus/Standard input files

hgo_2fiber_std_uni.inp: Uniaxial tension; displacement control; C3D8, C3D20R, and C3D10 elements.
hgo_2fiber_std_uni_c3d10hs.inp: Uniaxial tension; displacement control; C3D8, C3D20R, and C3D10HS elements.
hgo_2fiber_uni_hybrid.inp: Uniaxial tension; displacement control; C3D8H, C3D20RH, and C3D10H elements.
hgo_2fiber_std_uniori.inp: Uniaxial tension; displacement control; orientation along nonglobal Cartesian system; C3D8, C3D20R, and C3D10 elements.
hgo_2fiber_std_uniori_c3d10hs.inp: Uniaxial tension; displacement control; orientation along nonglobal Cartesian system; C3D8, C3D20R, and C3D10HS elements.
hgo_3fiber_std_uni.inp: Uniaxial tension; displacement control; C3D8 element.
hgo_3fiber_uni_c3d8h.inp: Uniaxial tension; displacement control; C3D8H element.
hgo_c3d8_std_ss.inp: Simple shear; displacement control; C3D8 element.
hgo_c3d8_std_uni.inp: Cyclic uniaxial tension; displacement control; C3D8 element.
hgo_2fiber_ehgc.inp: Simple shear; displacement control; C3D8, C3D8R, and CPE4R elements.
hgo_2fiber_pless.inp: Simple shear; displacement control; C3D8H, C3D8RH, and CPE4RH elements.
hgo_2fiber_ps.inp: Uniaxial tension; plane stress; load control; C3D8RH, CPS4R, S4R, and M3D4R elements.
hzplaniso_ve.inp: Viscoelastic behavior included; uniaxial tension, loading and unloading; C3D8R, CPE4R, and CPS4R elements.
uaniso_inv_hgople.inp: Plane strain tension/compression; user subroutine UANISOHYPER_INV verified using built-in Holzapfel strain energy function; displacement control; C3D8, CPE8R, and CPEG4 elements.
uaniso_inv_isople.inp: Plane strain tension; user subroutine UANISOHYPER_INV verified using built-in isotropic hyperelasticity; displacement control; C3D8H and CPE4H elements.

Abaqus/Explicit input files

holzapfel_disp_xpl.inp: Uniaxial cyclic test; displacement control; C3D8R, CPE4R, CPS4R, M3D4R, and S4R elements.
holzapfel_load_xpl.inp: Uniaxial cyclic test; load control; C3D8R, CPE4R, CPS4R, M3D4R, and S4R elements.
holzapfel_visco_xpl.inp: Combination with viscoelastic and Mullins effect; uniaxial cyclic test; C3D8R, CPE4R, CPS4R, M3D4R, and S4R elements.
xx_x1_holzapfel_disp.inp: Base problem for carrying out import from Abaqus/Explicit to Abaqus/Explicit. Uniaxial cyclic test; displacement control; C3D8R, CPE4R, CPS4R, M3D4R, and S4R elements.
xx_x2_holzapfel_disp_n_y.inp: Continuation of xx_x1_holzapfel_disp.inp with state imported.
xx_x1_holzapfel_load.inp: Base problem for carrying out import from Abaqus/Explicit to Abaqus/Explicit. Uniaxial cyclic test; load control; C3D8R, CPE4R, CPS4R, M3D4R, and S4R elements.
xx_x2_holzapfel_load_n_y.inp: Continuation of xx_x1_holzapfel_load.inp with state imported.
xx_x1_holzapfel_visco.inp: Base problem for carrying out import from Abaqus/Explicit to Abaqus/Explicit. Combination with viscoelastic and Mullins effect; uniaxial cyclic test; C3D8R, CPE4R, CPS4R, M3D4R, and S4R elements.
xx_x2_holzapfel_visco_n_y.inp: Continuation of xx_x1_holzapfel_visco.inp with state imported.

No compression

Elements tested

CPE4

Problem description

This option is used to modify the elasticity definition so that no compressive stress is allowed.

Material:


Young's modulus, E = 3.0e6
Poisson's ratio, $ν$ = 0.3

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

melnco1euc.inp: NO COMPRESSION, CPE4 elements.

No tension

Elements tested

CPE4

Problem description

This option is used to modify the elasticity definition so that no tensile stress is allowed.

Material:


Young's modulus, E = 3.0e6
Poisson's ratio, $ν$ = 0.3

Results and discussion

The results agree well with exact analytical or approximate solutions.

Input files

melnto1hut.inp: NO TENSION, CPE4 elements.

Compression factor with traction elastic behavior

Elements tested

COH2D4

COH3D8

Problem description

This option is used to modify the elasticity definition for uncoupled traction-separation elastic behavior such that the stiffness in compression is a user-specified factor times the stiffness in tension. Two cohesive elements are tested in each model. One element is subjected to a tensile strain (separation), while the other element is subjected to a compressive strain (separation).

Material:


Stiffness in normal direction, $E_{n n}$ = 2.0e5
Compression factor = 2.0

Results and discussion

The results agree well with exact analytical solutions.

Input files

Abaqus/Standard input files

coh2d4_compfac.inp: COH2D4 elements.
coh3d8_compfac.inp: COH3D8 elements.

Abaqus/Explicit input files

coh2d4_compfac_xpl.inp: COH2D4 elements.
coh3d8_compfac_xpl.inp: COH3D8 elements.