# Elasto-plastic Hydrodynamic Materials (LAW3)

This law is only used with solid brick and quadrilateral elements.

It models the elastic and plastic regions, similar to LAW2, with a nonlinear behavior of pressure and without strain rate effect. The law is designed to simulate materials in compression.

The stress-strain relationship for the material under tension is:(1)
$\sigma =\left(a+b{\epsilon }_{p}{}^{n}\right)$

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

Input requires Young's or the elastic modulus, $E$ , and Poisson's ratio, $\upsilon$ . These quantities are used only for the deviatoric part. The plasticity material parameters are:
$a$
Yield stress
$b$
Hardening modulus
$n$
Hardening exponent
${\sigma }_{\mathrm{max}}$
Maximum flow stress
${\epsilon }_{p}^{max}$
Plastic strain at rupture
A pressure cut off, Pmin, can be given to limit the pressure in tension. The pressure cut off must be lower or equal to zero. 図 1 shows a typical curve of the hydrodynamic pressure.