Isotropic Plastic Softening Material

Constitutive Law

This MPM Material is an isotropic, elastic-plastic material that can also develop anisotropic damage.

In the absence of damage, this material is identical to an Isotropic, Elastic-Plastic Material. In the absence of plasticity, this material is identical to an Isotropic Softening Material. If conditions allow, the material can develop both plasticity and damage with softening. Note that if plastic yield properties are below damage initiation stress, the material may never reach stress to cause damage. But, if the plastic properties allow hardening, the material can yield first and then start damage after hardening allows stresses to reach stress for initiation of damage.

Material Properties

For material properties, combine all options available for an Isotropic, Elastic-Plastic Material and for an Isotropic Softening Material. This material must, however, use large rotation mode (as is also required for an Isotropic Softening Material).

Property	Description	Units	Default
(Isotropic Properties)	Enter all properties needed to define the underlying isotropic material response	varies	varies
(Isotropic, Plastic Properties)	Enter yield properties and a hardening law, but cannot use a hardening law that changes shear modulus (Steinberg-Cochran-Guinan Hardening or Steinberg-Lund Hardening)	varies	varies
(Isotropic Softening Properties)	Enter properties for initiation of damage and for two softening laws	varies	varies
(other)	Properties common to all materials and must use the large rotation option	varies	varies

History Variables

The chosen hardening law will have at least one history variable and will start with history variable number 1. After the hardening law history variables, the remaining variables will be the same as for the Isotropic Softening Material material, but the history variable will be offset by the number of hardening law history variables. Because plastic strain is used for plasticity, three additional history variables (compared to an Isotropic Softening Material) track the three components of cracking strains in the crack axis system corresponding to normal and shear crack opening displacements.

Let P and S be number of history variables for the plastic law in use and for damage needed by an Isotropic Softening Material, respectively. The history variables for this material are then:

• 1 to P: Plastic law history variables
• P+1 to P+S: Isotropic Softening Material history variables
  • P+10: In 2D has total dissipated energy by damage mechanics (in Energy units))
• P+S+1: ε_c,xx or x direction cracking strain normal to crack in the crack axis system
• P+S+2: γ_c,xy or x-y direction shear cracking strain in the crack axis system
• P+S+3: γ_c,xz or x-z direction shear cracking strain in the crack axis system

For example when P=1 and S=13, this material defines 17 history variables. This material also tracks plastic strain, which can be saved by using the plasticstrain archiving option. The total plastic strain is archived in the global axis system.

If you also archive the damagenormal, you will be able to plot a vector along the crack-opening displacement vector.

Examples

Material "isoplastsoft","Isotropic Plastic Softening Material",53
  E 1000
  nu .33
  a 60
  rho 1
  largeRotation 1
  Initiation MaxPrinciple
  sigmac 30
  tauc 20
  SofteningI Linear
  I-Gc 10000
  SofteningII Linear
  II-Gc 10000
  Hardening Linear
  yield 20
  Ep 200
Done