Isotropic Plastic Softening Material

Constitutive Law

This MPM Material is an isotropic, elastic-plastic material that can also develop aniostropic damage. The material is available only in OSParticulas.

In the absense 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 have never reach stress to cause damage. But, if the plastic properties had 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 to an Isotropic, Elastic-Plastic Material and to 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, Elastic-Plastic Properties)	Enter yield properties and a hardening law	varies	varies
(Isotropic Softening Material)	Enter damage properties for initiation and for softening laws	varies	varies
(other)	Properties common to all materials	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 for the Isotropic Softening Material material. The softening history variable will be offset by the number of hardening law history variables.

In particle properties, the "plastic strain" will have sum of plastic strain due to plasticity and cracking strains due to anisotropic damage. In addition, the softening hisroty variables will have three addition variables for three components of cracking strains in the crack axis system corresponding to normal and shear crack opening displacements. By number withing Isotropic Softening Material history variables:

1. exx

The first history variables apply to the Isotropic, Elastic-Plastic Material

This material stores several history variables that track the extent of the damage and orientation of the damage plane:

1. 0, 0.9, 1.1, 1.9, or 2.1 to indicate undamaged (0), damage propagation (0.9 or 1.1), or post failure (decohesion) state of the particle (1.9 or 2.1). 0.9 and 1.9 indicate the failure initiated by tensile strength while 1.1 and 2.1 indicate failure initiated by shear strength.
2. δ_n or the maximum normal cracking strain.
3. δ_xy or the maximum x-y shear cracking strain.
4. δ_xz or the maximum x-z cracking strain (zero for 2D).
5. d_n or damage variable for normal loading. It varies from 0 to 1 where 1 is complete damage or failure.
6. d_xy or damage variable for x-y shear loading. It varies from 0 to 1 where 1 is complete damage or failure.
7. d_xz or damage variable for x-z shear loading. It varies from 0 to 1 where 1 is complete damage or failure (zero for 2D).
8. For 2D it is cos(θ), but for 3D it is Euler angle α.
9. For 2D it is sin(θ), but for 3D it is Euler angle β.
10. For 2D it is not used, but for 3D it is Euler angle γ.
11. A_c/V_p where A_c is crack area within the particle and V_p is particle volume.
12. Relative strength derived at the start by strengthCoefVariation property.

Variables 8-10 define the normal to the damage crack plane. For 2D, θ is the counter clockwise angle from the x axis to the crack normal. For 3D, (α, β, γ) are the three Euler angles for the normal direction using a Z-Y-Z rotation scheme. You can use the damagenormal archiving option to save enough information for plotting the normal. Although damaged normal is a unit vector, it is archived with magnitude equal to A_c/V_p (which gets another history variable archived and the value is used for some visualization options).

This material also tracks the cracking strain which can be saved by using the plasticstrain archiving option. The 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 "isosoft","Isotropic Softening Material",50
  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
Done