UMAT and UHYPER

User subroutine for isotropic Mises plasticity model

Elements tested

C3D8

Problem description

This set of verification problems tests many of the variables that are passed into UMAT, such as material properties, step times, and strain increment data. These tests also verify that the user-defined quantities of stresses, solution-dependent variables, and the Jacobian matrix are properly transferred to the solution process. These tests are modifications of the tests described in Rate-independent plasticity. Wherever an elastic-plastic material was defined in those tests, a user-defined material has been implemented in its place. The structure being analyzed is a cube made of a single C3D8 element.

Material:

Elasticity

Young's modulus, E = 200.0E3

Poisson's ratio, $ν$ = 0.3

Plasticity

Hardening:

Yield stress	Plastic strain
200.	0.0000
220.	0.0009
220.	0.0029

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 constitutive path is integrated with 20 increments of fixed size.

Input files

umatmst3.inp: Mises plasticity, uniaxial tension, three-dimensional solid.
umatmst3.f: User subroutine UMAT used in umatmst3.inp.
umatmss3.inp: Mises plasticity, simple shear, three-dimensional solid.
umatmss3.f: User subroutine UMAT used in umatmss3.inp.

User subroutine for hyperelastic model

Elements tested

C3D8

CPE4

Problem description

This set of verification problems is primarily intended to test the deformation gradient that is passed into UMAT. Variables in subroutine UHYPER that are functions of the deformation gradient are also tested. The structure being analyzed for the two-dimensional case is a unit square made up of three coincident CPE4 elements. The three-dimensional case consists of a cube of unit dimensions made up of three coincident C3D8 elements. For both cases the material properties of the first element are specified directly with general hyperelastic material properites. The same material properties are defined for the second and third elements through user subroutines UMAT and UHYPER, respectively. The displacements are prescribed at each of the nodes of the models, thus the stresses induced in each element will be the same.

Material:

Hyperelasticity: Mooney-Rivlin

$C_{10}$ = 80.0

$C_{01}$ = 0.0

$D_{1}$ = 2.013E−4

Results and discussion

The tests in this section are set up as cases of homogeneous deformation of three elements of unit dimensions. Consequently, the results are identical for all integration points within each of the elements. In each case the constitutive path is integrated with 10 increments of fixed size.

Input files

umathrt2.inp: Hyperelasticity, uniaxial tension, two-dimensional solid.
umathrt2.f: User subroutines UMAT and UHYPER used in umathrt2.inp.
umathrs2.inp: Hyperelasticity, simple shear, two-dimensional solid.
umathrs2.f: User subroutines UMAT and UHYPER used in umathrs2.inp.
umathrt3.inp: Hyperelasticity, uniaxial tension, three-dimensional solid.
umathrt3.f: User subroutines UMAT and UHYPER used in umathrt3.inp.
umathrs3.inp: Hyperelasticity, simple shear, three-dimensional solid.
umathrs3.f: User subroutines UMAT and UHYPER used in umathrs3.inp.

User subroutine for total and incompressible hybrid formulations

Elements tested

C3D8H

Problem description

This set of verification problems is primarily intended to test the total and incompressible hybrid formulations with user subroutine UMAT.

Material:

Hyperelasticity: neo-Hookean

$C_{10}$ = 100.0

$D_{1}$ = 1.E-03 or $D_{1}$ = 0

Results and discussion

The tests in this section are set up as cases of homogeneous deformation. For each case the results are compared against native Abaqus models and are found to be identical to the latter.

Input files

mhncdo3gsh_umat.inp: Almost incompressible hyperelasticity, planar tension, three-dimensional solid.
mhncdo3gsh_umat.f: User subroutine UMAT used in mhncdo3gsh_umat.inp.
mhncoo3hut_umat.inp: Fully incompressible hyperelasticity, uniaxial tension, three-dimensional solid.
mhncoo3hut_umat.f: User subroutine UMAT used in mhncoo3hut_umat.inp.

User subroutine for frequency domain viscoelastic behavior

Elements tested

C3D8

Problem description

This verification problem is primarily intended to test the implementation of frequency domain viscoelastic behavior in user subroutine UMAT in terms of the storage modulus (stiffness) and loss modulus (damping).

Material:

Linear elastic: viscoelastic

$E$ = 200.E+09, $ν$ = 0.3

$(ω ℜ (g^{*}) = G_{ℓ} / G_{\infty})$ = 1.775E-03.

$(ω ℑ (g *) = 1 - G_{s} / G_{\infty})$ = –5.116E-03

Results and discussion

The test involves the steady-state dynamic response of a cantilever beam subjected to pressure load. The results are compared to a similar model that uses a native Abaqus material model. The results for the two problems are identical.

Input files

visco_freqdmn_umat_ssd.inp: Cantilever beam modeled with C3D8 elements.
visco_freqdmn_umat_ssd.f: User subroutine UMAT used in visco_freqdmn_umat_ssd.inp.

Additional user subroutine problems for hyperelastic model

Elements tested

C3D8RH

CPS4R

Problem description

This set of verification problems is primarily intended to test the variables that are passed into UHYPER. In each test the material properties are specified using general hyperelastic material properties for the first element and the strain energy function and the associated derivatives defined in user subroutine UHYPER for the second element. Three different sets of material data are used, as described below.

Material 1

Polynomial (N=1), compressible

$C_{10}$ = 80.0

$C_{01}$ = 20.0

$D_{1}$ = 1.E−3

Material 2

Polynomial (N=1), compressible, field variable dependency included for UHYPER

$C_{10}$ = 80.0

$C_{01}$ = 20.0

$D_{1}$ = 1.5E−3

Material 3

Polynomial (N=1), incompressible, temperature dependency included

$θ$ = 0.0, $C_{10}$ = 80.0, $C_{01}$ = 20.0

$θ$ = 20.0, $C_{10}$ = 75.0, $C_{01}$ = 18.0

$θ$ = 30.0, $C_{10}$ = 70.0, $C_{01}$ = 16.0

Results and discussion

Since the same boundary conditions are applied on the corresponding nodes of the two elements, the results are expected to be identical in the two cases, thus verifying the use of UHYPER with the second element.

Input files

uhypercp2s.inp: Compressible, biaxial tension, 2D, state variables, Material 1.
uhypercp2s.f: User subroutine UHYPER used in uhypercp2s.inp.
uhyperct3f.inp: Compressible, uniaxial tension, 3D, field variables, Material 2.
uhyperct3f.f: User subroutine UHYPER used in uhyperct3f.inp.
uhyperip2t.inp: Incompressible, biaxial tension, 2D, temperature dependency, Material 3.
uhyperip2t.f: User subroutine UHYPER used in uhyperip2t.inp.
uhyperip3t.inp: Incompressible, biaxial tension, 3D, temperature dependency, Material 3.
uhyperip3t.f: User subroutine UHYPER used in uhyperip3t.inp.

UMAT and UHYPER

Features tested

User subroutine for isotropic Mises plasticity model

Elements tested

Problem description

Material:

Results and discussion

Input files

User subroutine for hyperelastic model

Elements tested

Problem description

Material:

Results and discussion

Input files

User subroutine for total and incompressible hybrid formulations

Elements tested

Problem description

Material:

Results and discussion

Input files

User subroutine for frequency domain viscoelastic behavior

Elements tested

Problem description

Material:

Results and discussion

Input files

Additional user subroutine problems for hyperelastic model

Elements tested

Problem description

Material 1

Material 2

Material 3

Results and discussion

Input files