Description
This is constitutive model for ductile metals with optional thermal softening and strain rate hardening.
The effective plastic flow stress is defined as:
$\displaystyle{ \sigma_y = f(\epsilon_{eff}^p) \cdot g(D) \cdot \left( 1 - \left( \frac{T-T_0}{T_m - T_0}\right)^m \right) \cdot
\left( 1 + \frac{\dot{\epsilon}_{eff}^p}{\dot{\epsilon}_0} \right)^c}$
where $f(\epsilon_{eff}^p)$ 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 $\mu \gt 0$:
$\displaystyle{ \sigma_y = f(\epsilon_{eff}^p) \cdot g(D) \cdot \left( 1 - \left( \frac{T-T_0}{T_m - T_0}\right)^m \right) +
\mu \left( \frac{\dot{\epsilon}_{eff}^p}{\dot{\epsilon}_0} \right)^c}$
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:
$p = -K \epsilon_v + 3K \alpha_T (T-T_{ref})$
where $K$ is the bulk modulus, $\epsilon_v$ is the volumetric strain.
$\alpha_T$ is the thermal expansion coefficient and $T_{ref}$ is the reference temperature (see PROP_THERMAL).
