MAT_STEINBERG_GUINAN
FE
Material properties
"Optional title"
mid, $\rho_0$, $G_0$, $K_0$, did, tid, eosid
$Y_0$, $Y_{max}$, $\beta$, $n$, $\varepsilon_i$, $G_p$, $G_T$, $Y_p$
$T_0$, $T_{m0}$, $a$
Parameter definition
Description
A rate-independent, high-rate Steinberg-Guinan metal model with von Mises plasticity. It implements the pressure-, temperature-, density- and plastic-strain-dependent strength formulation of Steinberg, Cochran and Guinan, A constitutive model for metals applicable at high-strain rate, Journal of Applied Physics 51(3), 1498--1504 (1980).
The model uses $\eta=V_0/V=\rho/\rho_0$, the thermodynamic pressure $p$ supplied by EOS_GRUNEISEN, and the current material temperature $T$. The shear modulus is evaluated as:
$\displaystyle{G=\mathrm{max}\left(0, G_0 + G_p p\eta^{-1/3} + G_T(T-T_0)\right)}$
Isotropic hardening is capped at $Y_{max}$:
$\displaystyle{Y_h=\mathrm{min}\left[Y_0\left(1+\beta(\varepsilon_i+\varepsilon_{eff}^p)\right)^n,Y_{max}\right]}$
The current yield strength used by the radial-return update is:
$\displaystyle{\sigma_y=\mathrm{max}\left\{0,Y_h\left[1+\frac{Y_p}{Y_0}p\eta^{-1/3}+\frac{G_T}{G_0}(T-T_0)\right]\right\}}$
The melt temperature evolves with compression according to:
$\displaystyle{T_m=T_{m0}\,\mathrm{exp}\left[2a\left(1-\eta^{-1}\right)\right]\eta^{2(\Gamma_0-a-1/3)}}$
Here $\Gamma_0$ is the Gruneisen coefficient from EOS_GRUNEISEN. At or above $T_m$, or when the calculated shear modulus is zero, the model removes deviatoric strength. Plastic work is converted to heat using the heat-capacity and plastic-work conversion data from PROP_THERMAL.
$\rho_0$, $G_0$, $K_0$, $Y_0$, $T_0$ and $T_{m0}$ must be positive; $Y_{max}\geq Y_0$, $T_{m0}>T_0$, and $\beta$, $n$, $\varepsilon_i$ and $a$ must be non-negative. The referenced thermal property must provide a positive heat capacity (constant or CURVE), and the referenced Gruneisen EOS must have a positive $\Gamma_0$.
