#### Command list

• Input handling
• Solution control and techniques
• Output
• Mesh commands
• Nodes and connectivity
• Material properties
• Initial conditions
• Boundary conditions
• Contact and tied interfaces
• Rigid bodies
• Connectors
• Parameters and functions
• Geometries
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• Coordinate system
• Particle
• SPH

### MAT_STEINBERG_GUINAN

###### SPH
Attention: This command is in the beta stage and the format may change over time.
*MAT_STEINBERG_GUINAN
"Optional title"
mid, $\rho$, $G_0$, $\nu$, did, tid, eosid
$\sigma_0$, $\beta$, $n$, $\varepsilon_i$, $G'_p$, $G'_t$, $\sigma_{max}$, $T_{m0}$
$\Gamma_0$, $a$

#### Parameter definition

VariableDescription
mid Unique material identification number
$\rho$ Density
$G_0$ Shear modulus
$\nu$ Poisson's ratio
did Damage property command ID
tid Thermal property command ID
eosid Equation-of-state ID
$\sigma_0$ Initial yield stress
$\beta$ Work hardening parameter
$n$ Work hardening parameter
$\varepsilon_i$ Initial equivalent plastic strain
$G'_p$ The pressure derivative of $G$ at the reference state
$G'_t$ The temperature derivative of $G$ at the reference state
$\sigma_{max}$ Flow stress cap
$T_{m0}$ Initial melting temperature
$\Gamma_0$ Reference Gruneisen $\Gamma$
$a$ Pressure dependency coefficient

#### Description

This command is only supported by $\gamma SPH$. The shear modulus is defined as:

$\displaystyle{G = G_0 \left[ 1 + \frac{G'_p}{G_0} \frac{\mathrm{max}(p,0)}{\eta^{1/3}} + \frac{G'_t}{G_0} \mathrm{max}(T-T_0,0) \right] }$

where $\eta = \rho/\rho_0$. The flow stress (von Mises) is:

$\displaystyle{\sigma = \mathrm{min} \left( \sigma_{max}, \sigma_0 \left[ 1 + \beta (\varepsilon_{eff}^p + \varepsilon_i) \right]^n \right) \frac{G}{G_0} }$

The melting temperature is defined as:

$\displaystyle{T_m = T_{m0} \eta^{\left[2(\Gamma_0 - a - \frac{1}{3})\right]} \cdot \mathrm{e}^{2a \left( 1 - \frac{1}{\eta} \right) }}$

At temperatures $T \gt T_m$, $G=0$ and $\sigma=0$.