Johnson-Cook Law for Hydrodynamics (LAW4)

This law enables to model hydrodynamic behavior of an elastic-plastic material using Johnson-Cook Yield criteria and any equation of state available with /EOS card. It based on /MAT/LAW3 and adds strain rate and temperature dependency. The advantage of material LAW04 regarding classical LAW02 (/MAT/JCOOK) is that you can choose any available EOS from /EOS card.

The equation describing yield stress (scale value) is:(1)

σ_{y} = (A + {B ε}_{p}^{n}) (1 + C ln \frac{\dot{ε}}{\dot{ε_{0}}}) (1 - T^{*}^{m})

Where, $T^{*} = \frac{T - T_{r}}{T_{m e l t} - T_{r}}$

The pressure and energy values are obtained by solving equation of state $P (μ, E)$ related to the material (/EOS).

Material parameters are the same as in LAW3.

The parameters are:

$C$: Strain rate coefficient
${\dot{ε}}_{0}$: Reference strain rate
$m$: Temperature exponent
T_melt: Melting temperature
T_max: Maximum temperature; For $T > T_{\max}$ , then $m$ =1 is used.
$ρ_{0} C_{p}$: Specific heat per unit volume

For an explanation about strain rate filtering, refer to Strain Rate Filtering.