# Steinberg-Guinan Material (LAW49)

This law defines as elastic-plastic material with thermal softening. When material approaches melting point, the yield strength and shear modulus reduces to zero.

The melting energy is defined as:

${E}_{m}={E}_{c}+\rho {c}_{p}{T}_{m}$

Where, ${E}_{c}$ is cold compression energy and ${T}_{m}$ melting temperature is supposed to be constant. If the internal energy $E$ is less than ${E}_{m}$ , the shear modulus and the yield strength are defined by:

$G={G}_{0}\left[1+{b}_{1}p{V}^{1}{3}}-h\left(T-{T}_{0}\right)\right]{e}^{-\frac{fE}{E-{E}_{m}}}$
${\sigma }_{y}={{\sigma }^{\prime }}_{0}\left[1+{b}_{2}p{V}^{1}{3}}-h\left(T-{T}_{0}\right)\right]{e}^{-\frac{fE}{E-{E}_{m}}}$

Where, ${b}_{1}$ , ${b}_{2}$ , $h$ and $f$ are the material parameters. ${{\sigma }^{\prime }}_{0}$ is given by a hardening rule:

${{\sigma }^{\prime }}_{0}={\sigma }_{0}{\left[1+\beta {\epsilon }_{p}\right]}^{n}$

The value of ${{\sigma }^{\prime }}_{0}$ is limited by ${\sigma }_{\mathrm{max}}$ .

The material pressure $p$ is obtained by solving equation of state $P\left(\mu ,E\right)$ related to the material (/EOS) as in LAW3.