Isotropic, Hyperelastic-Plastic Mie-Grüneisen Material

Constitutive Law

This MPM material is identical to an HEIsotropic material except that it uses a Mie-Grüneisen equation of state in the elastic regime. The elastic shear stress is handled using 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 HEIsotropic material except that it uses a 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

Material "copper","Copper","HEMGEOSMaterial"
  C0 3933
  S1 1.5
  gamma0 1.99
  rho 8.93
  G 48000
  Cv 134
  kCond 401
  hardening "JohnsonCook"
  Ajc 90
  Bjc 292
  njc .31
  Cjc 0.025
  ep0jc 1
  Tmjc 1356
  mjc 1.09
Done

Material "pmma","PMMA","HEMGEOSMaterial"
  C0 2300
  S1 1.82
  gamma0 1.82
  rho 1.18
  G 1075
  Cv 1466
  kCond 0.2
  hardening "Linear"
  yield 40
  Ep 1500
Done