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 $$\sigma_{ij} = S_{ij} + \delta_{ij} P$$ The following equation which associates the stress deviator tensor ($s_{ij}$) and the strain rate deviator tensor ($D_{ij}$) is

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

For a newtonian fluid : $m=1 \rightarrow S_{ij} = 2 \mu D_{ij}$

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

Norton-Hoff law including thermal aspects.