Material law describing a non viscous fluid.

Stresses are computed with

$$\sigma_{ij} = s_{ij} + \delta_{ij} p$$ with $s_{ij} = 0$ in a non viscous fluid.

The equation which associates pressure and volume is $$dP = -K \frac{dV}{V}$$ where $K$ is the bulk modulus.

Norton-Hoff law descriding a viscous fluid.

Stresses are computed with $$\sigma_{ij} = s_{ij} + p \delta_{ij}$$

where $p$ is the hydrostatic pressure and $s_{ij}$ the stress deviator tensor.

The stress deviator tensor ($s_{ij}$) is determined upon the strain rate deviator tensor ($D_{ij}$) through the following equation

$$s_{ij} = 2 \mu D_{ij} \left( \sqrt{3} \ \sqrt{\frac{2}{3} D_{wz}.D_{wz}} \right)^{m-1}$$

Hydrostatic pressure is computed upon volume variation through the following eqation

$$dp = K \frac{dV}{V}$$

where $K$ is the bulk modulus and $V$ the volume.

Norton-Hoff law including thermal aspects.