Recovering convexity in non-associated plasticity

Gilles A. Francfort

doi:10.1016/j.crme.2017.12.005

The legacy of Jean-Jacques Moreau in mechanics

Recovering convexity in non-associated plasticity

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

Comptes Rendus. Mécanique, Volume 346 (2018) no. 3, pp. 198-205.

Abstract

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.

Received: 2017-05-20
Accepted: 2017-10-11
Published online: 2017-12-06

DOI: 10.1016/j.crme.2017.12.005

Keywords: Elasto-plasticity, Non-associated flow rules, Quasi-static evolution, Convex analysis

Author's affiliations:

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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     title = {Recovering convexity in non-associated plasticity},
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     pages = {198--205},
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     doi = {10.1016/j.crme.2017.12.005},
     language = {en},
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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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