Norton behaviour description

This viscoplastic behaviour is fully determined by the evolution of the equivalent viscoplastic strain \(p\) as a function \(f\) of the Von Mises stress \({\sigma_{\mathrm{eq}}}\) : \[\dot{p}=f{\left({\sigma_{\mathrm{eq}}}\right)}=A\,{\sigma_{\mathrm{eq}}}^{E}\]

where :

\(A\) and \(E\) are declared as material properties .

List of supported Hypotheses

Variables

Material properties

State variables

Parameters

Parameters

Local variables

Code documentation

FlowRule description

The return-mapping algorithm used to integrate this behaviour requires the definition of \(f\) and \({{\displaystyle \frac{\displaystyle \partial f}{\displaystyle \partial {\sigma_{\mathrm{eq}}}}}}\) (see Simo and Hughes (1998) and Helfer et al. (2013) for details).

We introduce an auxiliary variable called tmp to limit the number of call to the pow function

Helfer, Thomas, Étienne Castelier, Victor Blanc, and Jérôme Julien. 2013. “Le Générateur de Code Mfront : Écriture de Lois de Comportement Mécanique.” Note technique 13-020. CEA DEN/DEC/SESC/LSC.

Simo, Juan C, and Thomas J. R Hughes. 1998. Computational Inelasticity. New York: Springer.