#### MAT_METAL

###### Material properties
*MAT_METAL
"Optional title"
mid, $\rho$, $E$, $\nu$, did, tid, eosid
cid, $\xi$, tresca, $c$, $\dot\varepsilon_0$, $m$, $T_0$, $T_m$
$s_0$, $s_1$, $\varepsilon_d$, $\mu$
##### Parameter definition
VariableDescription
mid Unique material identification number
$\rho$ Density
$E$ Young's modulus
$\nu$ Poisson's ratio
did Damage property command ID
tid Thermal property command ID
eosid Equation-of-state ID
cid ID of a CURVE or FUNCTION defining plastic flow stress versus plastic strain (equivalent measures)
$\xi$ Kinematical hardening parameter ranging from 0 to 1
default: 0 (pure iso-tropic hardening)
tresca Flag to activate Tresca yield criterion
options:
0 $\rightarrow$ von Mises
1 $\rightarrow$ Tresca
$c$ Strain rate hardening parameter
default: 0
$\dot\varepsilon_0$ Reference strain rate
default: 1
$m$ Thermal softening parameter
default: thermal softening deactivated
$T_0$ Thermal softening reference temperature
default: 0
$T_m$ Melting temperature
default: 1.0d20
$s_0$ Damage softening parameter (threshold damage level)
default: not used
$s_1$ Damage softening parameter
$\varepsilon_d$ Dilatation (void fraction) at full damage
$\mu$ Optional rate parameter (SPH only)
default: not used
##### Description

This is constitutive model for ductile metals with optional thermal softening and strain rate hardening. The effective plastic flow stress is defined as:

$\displaystyle{ \sigma_y = f(\varepsilon_{eff}^p) \cdot g(D) \cdot \left( 1 - \left( \frac{T-T_0}{T_m - T_0}\right)^m \right) \cdot \left( 1 + \frac{\dot{\varepsilon}_{eff}^p}{\dot{\varepsilon}_0} \right)^c}$

where $f(\varepsilon_{eff}^p)$ is a user defined CURVE or FUNCTION, $g(D)$ is an optional damage softening and $T$ is the current temperature. $g(D)$, 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). There is a special SPH (PARTICLE_SPH) version of this material model, with an optional strain and temperature independent strain rate hardening. It is activated by specifying $\mu \gt 0$:

$\displaystyle{ \sigma_y = f(\varepsilon_{eff}^p) \cdot g(D) \cdot \left( 1 - \left( \frac{T-T_0}{T_m - T_0}\right)^m \right) + \mu \left( \frac{\dot{\varepsilon}_{eff}^p}{\dot{\varepsilon}_0} \right)^c}$

This variant has been developed specifically for shaped charge jets that can exhibit strong strain rate effects at high temperatures.

The hydrostatic pressure $p$ is defined as:

$p = -K \varepsilon_v + 3K \alpha_T (T-T_{ref})$

where $K$ is the bulk modulus, $\varepsilon_v$ is the volumetric strain. $\alpha_T$ is the thermal expansion coefficient and $T_{ref}$ is the reference temperature (see PROP_THERMAL).