Steinberg-Guinan Material (LAW49)

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} + ρ 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} [1 + b_{1} p V^{\frac{1}{3}} - h (T - T_{0})] e^{- \frac{f E}{E - E_{m}}}

(3)

σ_{y} = {σ^{'}}_{0} [1 + b_{2} p V^{\frac{1}{3}} - h (T - T_{0})] e^{- \frac{f E}{E - E_{m}}}

Where,

b_{1}

b_{2}

h

and

f

are the material parameters.

{σ^{'}}_{0}

is given by a hardening rule:(4)

{σ^{'}}_{0} = σ_{0} {[1 + β ε_{p}]}^{n}

The value of ${σ^{'}}_{0}$ is limited by $σ_{\max}$ .

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