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

The melting energy is defined as:

(1)
$${E}_{m}={E}_{c}+\rho {c}_{p}{T}_{m}$$

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:

(2)
$$G={G}_{0}\left[1+{b}_{1}p{V}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}-h\left(T-{T}_{0}\right)\right]{e}^{-\frac{fE}{E-{E}_{m}}}$$

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

Where,

${b}_{1}$
,

${b}_{2}$
,

$h$
and

$f$
are the material parameters.

${{\sigma}^{\prime}}_{0}$
is given by a hardening rule:

(4)
$${{\sigma}^{\prime}}_{0}={\sigma}_{0}{\left[1+\beta {\epsilon}_{p}\right]}^{n}$$

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.