Large-strain viscoelasticity with hyperelasticity

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

This page discusses:

Elements tested
Features tested
Problem description
Results and discussion
Input files
Figures

ProductsAbaqus/Explicit

Elements tested

CAX4R

CPE4R

CPS4R

M3D4R

Features tested

Large deformation kinematics, viscoelastic-hyperelastic material model.

Problem description

This example is used to verify the viscoelastic material model in Abaqus/Explicit. In all of the problems, the material is defined by the hyperelastic polynomial formulation with $N = 1$ . The viscoelastic behavior is given by Prony series parameters or by using the test data input option.

The first test is volumetric relaxation. A single element is compressed at a uniform rate over a period of time during which the stresses are allowed to relax. This problem tests that the volumetric relaxation behavior is captured correctly. Plane stress and plane strain elements are used in this test.

The second test is uniaxial relaxation. A single element is stretched at a uniform rate over a period of time during which the stresses are allowed to relax. This problem verifies that the shear relaxation behavior is captured correctly. Plane strain and membrane elements are used in this test.

The third test is circumferential relaxation. All nodes of a single axisymmetric element are moved radially outward at a uniform rate over a period of time during which the stresses are allowed to relax. All the nodes are fixed in the axial direction. This problem verifies that the shear and volumetric relaxation behavior is correct in the circumferential direction.

Results and discussion

The time histories of the stresses are shown in Figure 1 through Figure 3. Figure 1 shows the volumetric response of the material with viscoelastic properties compared to the response without viscoelastic properties. Figure 2 shows the tensile response of the material with viscoelastic properties compared to the response without viscoelastic properties. Figure 3 shows the circumferential response of the material with viscoelastic properties compared to the response without viscoelastic properties.

This problem tests the features listed but does not provide independent verification of them.

Input files

visco_vol_pe.inp: Volumetric relaxation test using plane strain elements.
visco_uni_mem.inp: Uniaxial relaxation test using membrane elements.
visco_circum_axi.inp: Circumferential creep test using axisymmetric elements.
visco_vol_ps.inp: Volumetric relaxation test using plane stress elements.
visco_uni_pe.inp: Uniaxial relaxation test using plane strain elements.
visco_uni_pe_frq.inp: Uniaxial relaxation test using plane strain elements and using Prony parameters calibrated from frequency-dependent moduli data.

Figures