# 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:

Where, ${T}^{*}=\frac{T-{T}_{r}}{{T}_{melt}-{T}_{r}}$

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

Material parameters are the same as in LAW3.

- $C$
- Strain rate coefficient
- ${\dot{\epsilon}}_{0}$
- Reference strain rate
- $m$
- Temperature exponent
`T`_{melt}- Melting temperature
`T`_{max}- Maximum temperature
- $\rho {\text{\hspace{0.05em}}}_{0}{C}_{p}$
- Specific heat per unit volume

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