Product: ABAQUS/Standard
User subroutines to define isotropic Mises plasticity and Mooney-Rivlin 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 in ABAQUS/Standard,” Section 2.2.9. 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 the *HYPERELASTIC material option. 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 variables that are passed into UHYPER. In each test the material properties are specified using the material option *HYPERELASTIC for the first element and subsequently specified using the material option *HYPERELASTIC, USER for the second element; for the second element the strain energy function and the associated derivatives are defined in user subroutine UHYPER. 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, 2-D, state variables, Material 1.
User subroutine UHYPER used in uhypercp2s.inp.
Compressible, uniaxial tension, 3-D, field variables, Material 2.
User subroutine UHYPER used in uhyperct3f.inp.
Incompressible, biaxial tension, 2-D, temperature dependency, Material 3.
User subroutine UHYPER used in uhyperip2t.inp.
Incompressible, biaxial tension, 3-D, temperature dependency, Material 3.
User subroutine UHYPER used in uhyperip3t.inp.