Comptes Rendus
no. 3
The legacy of Jean-Jacques Moreau in mechanics
Recovering convexity in non-associated plasticity
Gilles A. Francfort1, 2
1 Université Paris-Nord, LAGA, avenue Jean-Baptiste-Clément, 93430 Villetaneuse, France
2 Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, USA
Comptes Rendus. Mécanique, Volume 346 (2018) no. 3, pp. 198-205.

We quickly review two main non-associated plasticity models, the Armstrong–Frederick model of nonlinear kinematic hardening and the Drucker–Prager cap model. Non-associativity is commonly thought to preclude any kind of variational formulation, be it in a Hencky-type (static) setting, or when considering a quasi-static evolution because non-associativity destroys convexity. We demonstrate that such an opinion is misguided: associativity (and convexity) can be restored at the expense of the introduction of state variable-dependent dissipation potentials.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2017.12.005
Mots clés : Elasto-plasticity, Non-associated flow rules, Quasi-static evolution, Convex analysis
Gilles A. Francfort 1, 2

1 Université Paris-Nord, LAGA, avenue Jean-Baptiste-Clément, 93430 Villetaneuse, France
2 Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, USA 
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Gilles A. Francfort. Recovering convexity in non-associated plasticity. Comptes Rendus. Mécanique, Volume 346 (2018) no. 3, pp. 198-205. doi : 10.1016/j.crme.2017.12.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.12.005/

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