MAT_METAL
Material properties
"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
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 an alternative version of this material model, with a strain and temperature independent strain rate hardening. It is activated by specifying $\mu \gt 0$:
$\displaystyle{ \sigma_y = f(\varepsilon_{eff}^p) \cdot g(D) \cdot \left( 1 - \left( \frac{T-T_0}{T_m - T_0}\right)^m \right) + \mu \left( \frac{\dot{\varepsilon}_{eff}^p}{\dot{\varepsilon}_0} \right)^c}$
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).
