#### MAT_JC

###### Material properties
*MAT_JC
"Optional title"
mid, $\rho$, $E$, $\nu$, did, tid, eosid
$A$, $B$, $n$, $C$, $m$, $T_0$, $T_m$, $\dot{\varepsilon}_0$
$C_p$, $k$, $d$, $e$
##### Parameter definition
VariableDescription
mid Unique material identification number
$\rho$ Density
$E$ Young's modulus
$\nu$ Poisson's ratio
did Damage property command ID
tid Thermal property command ID
eosid Equation-of-state ID
$A$ Initial yield strength
$B$ Hardening parameter
$n$ Hardening parameter
$C$ Strain rate hardening parameter
$m$ Thermal softening parameter
$T_0$ Ambient temperature
$T_m$ Melting temperature
$\dot{\varepsilon}_0$ Strain rate parameter
default: 1
$C_p$ Specific heat capacity
$k$ Plastic work to heat conversion factor
default: 0.9
$d$ Thermal softening parameter
default: 1.0
$e$ Thermal softening parameter
default: 1.0
##### Description

Johnson-Cook's constitutive model. The von Mises flow stress is defined as:

$\displaystyle{\sigma_y = \left( A + B(\varepsilon_{eff}^p)^n \right) \cdot \left( 1 + C \cdot \mathrm{ln}\left( \frac{\dot\varepsilon_{eff}^p}{\dot{\varepsilon}_0} \right) \right) \cdot \left(d - e \cdot \left( \frac{\mathrm{T}-\mathrm{T}_0}{\mathrm{T}_m - \mathrm{T}_0} \right)^m \right)}$

$T$ is the current temperature. The hydrostatic pressure $p$ is defined as:

$p = -K \varepsilon_v + 3K \alpha_T (T-T_{ref})$

where $K$ is the bulk modulus, $\varepsilon_v$ is the volumetric strain. $\alpha_T$ is the thermal expansion coefficient and $T_{ref}$ is the reference temperature (see PROP_THERMAL).