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)

σ = (a + b ε_{p}^{n})

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

Input requires Young's or the elastic modulus,

E

, and Poisson's ratio,

υ

. These quantities are used only for the deviatoric part. The plasticity material parameters are:

$a$: Yield stress
$b$: Hardening modulus
$n$: Hardening exponent
$σ_{\max}$: Maximum flow stress
$ε_{p}^{m a x}$: Plastic strain at rupture

A pressure cut off, P_min, can be given to limit the pressure in tension. The pressure cut off must be lower or equal to zero. Figure 1 shows a typical curve of the hydrodynamic pressure.