Product: Abaqus/Standard
User subroutines to define isotropic Mises plasticity, Mooney-Rivlin, and neo-Hookean hyperelastic material properties.
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,” Section 2.2.10. 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, 
= 0.3
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.
Mises plasticity, uniaxial tension, three-dimensional solid.
User subroutine UMAT used in umatmst3.inp.
Mises plasticity, simple shear, three-dimensional solid.
User subroutine UMAT used in umatmss3.inp.
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
= 80.0
= 0.0
= 2.013E–4
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.
Hyperelasticity, uniaxial tension, two-dimensional solid.
Hyperelasticity, simple shear, two-dimensional solid.
Hyperelasticity, uniaxial tension, three-dimensional solid.
Hyperelasticity, simple shear, three-dimensional solid.
This set of verification problems is primarily intended to test the total and incompressible hybrid formulations with user subroutine UMAT.
Material:
Hyperelasticity: neo-Hookean
= 100.0
= 1.E-03 or = 0
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.
Almost incompressible hyperelasticity, planar tension, three-dimensional solid.
User subroutine UMAT used in mhncdo3gsh_umat.inp.
Fully incompressible hyperelasticity, uniaxial tension, three-dimensional solid.
User subroutine UMAT used in mhncoo3hut_umat.inp.
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
= 200.E+09, = 0.3
= 1.775E-03.
= –5.116E-03
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.
Cantilever beam modeled with C3D8 elements.
User subroutine UMAT used in visco_freqdmn_umat_ssd.inp.
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
= 80.0
= 20.0
= 1.E–3
Material 2:
Polynomial (N=1), compressible, field variable dependency included for UHYPER
= 80.0
= 20.0
= 1.5E–3
Material 3:
Polynomial (N=1), incompressible, temperature dependency included
= 0.0, = 80.0, = 20.0
= 20.0, = 75.0, = 18.0
= 30.0, = 70.0, = 16.0
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.
Compressible, biaxial tension, 2D, state variables, Material 1.
User subroutine UHYPER used in uhypercp2s.inp.
Compressible, uniaxial tension, 3D, field variables, Material 2.
User subroutine UHYPER used in uhyperct3f.inp.
Incompressible, biaxial tension, 2D, temperature dependency, Material 3.
User subroutine UHYPER used in uhyperip2t.inp.
Incompressible, biaxial tension, 3D, temperature dependency, Material 3.
User subroutine UHYPER used in uhyperip3t.inp.