#### Command list

• Input handling
• Solution control and techniques
• Output
• Mesh commands
• Nodes and connectivity
• Material properties
• Initial conditions
• Boundary conditions
• Contact and tied interfaces
• Rigid bodies
• Connectors
• Parameters and functions
• Geometries
• Sets
• Coordinate system
• Particle
• SPH

### MAT_FORMING_R

###### Material properties
*MAT_FORMING_R
"Optional title"
mid, $\rho$, $E$, $\nu$, did, tid
cid, $\xi$, $R_{00}$, $R_{45}$, $R_{90}$, $s_0$, $s_1$

#### Parameter definition

VariableDescription
mid Unique material identification number
$\rho$ Density
$E$ Young's modulus
$\nu$ Poisson's ratio
did Damage model ID
tid Thermal property command ID
cid ID of a CURVE or FUNCTION defining effective plastic flow stress versus plastic strain (equivalent measures)
$\xi$ Kinematical hardening parameter ranging from 0 to 1
default: 0 (pure iso-tropic hardening)
$R_{00}$ Lankford coefficient
$R_{45}$ Lankford coefficient
$R_{90}$ Lankford coefficient
$s_0$ Damage softening parameter (threshold damage level)
default: $s_0 = 1$
$s_1$ Damage softening parameter

#### Description

This is a plasticity model where kinematical hardening and Lankford parameters can be defined as constants or as functions of the effective plastic strain. A J2 (von Mises) yield criterion is combined with a non-assiciated flow rule. The non-associated flow rule is defined to satisfy the given Lankford parameters.

The effective plastic flow stress is defined as:

$\displaystyle{ \sigma_y = f(\epsilon_{eff}^p) \cdot g(D)}$

where $f(\epsilon_{eff}^p)$ is a user defined CURVE or FUNCTION and $g(D)$ is an optional damage softening. $g(D)$, where $D$ is the damage level, is defined as:

$g(D) = \left\{ \begin{array}{cc} 1 & D \leq s_0 \\ \displaystyle{ 1 + \frac{D-s_0}{1-s_0} \cdot (s_1-1)} & D \gt s_0 \end{array} \right.$

That is, $g(D)$ drops linearly from 1 at $D=s_0$ to $s_1$ at $D=1$ (full damage).

Initial material orientation is defined using either INITIAL_MATERIAL_DIRECTION, INITIAL_MATERIAL_DIRECTION_VECTOR or INITIAL_MATERIAL_DIRECTION_WRAP.