## 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

Variable
Description
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).