MAT_STEINBERG_GUINAN
γSPH
Beta command
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
$\sigma_0$, $\beta$, $n$, $\varepsilon_i$, $G'_p$, $G'_t$, $\sigma_{max}$, $T_{m0}$
$\Gamma_0$, $a$
"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
Variable
Description
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 $\sigma=0$.
