Isotropic, Hyperelastic-Plastic Mie-Grüneisen Material

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Constitutive Law

This MPM material is identical to an HEIsotropic material in that it uses a Mie-Grüneisen equation of state in the elastic regime. The elastic shear terms are handles like the Neohookean shear terms in the HEIsotropic material. A small-strain version of this material is also available in a MGEOSMaterial material; this hyperelastic version is usually the preferable choice for accurate simulations.

Material Properties

The Mie-Grüneisen equation of state properties and the hardening law properties are set with the following options:

Property Description Units Default
C0 The bulk wave speed m/sec 4004
gamma0 The γ0 parameter none 1.64
S0 The S0 parameter none 1.35
S1 The S1 parameter none 0
S2 The S2 parameter none 0
G Low-strain shear modulus MPa none
Hardening This command selects the hardening law by its name or number. It should be before entering any yielding properties. none none
(yield) Enter all plasticity properties required by the selected hardening law. varies varies
(other) Properties common to all materials varies varies

History Variables

The selected hardening law will create one or more history variables. This material uses the next history variable (after the hardening laws history variables) to store the volumetric change (i.e., J or the determinant of the deformation gradient). The total strain is stored in the elastic strain variable, while the plastic strain stores the left Cauchy Green tensor.

Examples