Comptes Rendus
no. 6
Quasi-static response, implicit scheme and incremental problem in gradient plasticity
Quoc-Son Nguyen1
1 Laboratoire de Mécanique des Solides, École Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau, France
Comptes Rendus. Mécanique, Volume 344 (2016) no. 6, pp. 439-447.

This paper is devoted to the study of gradient plasticity at small strains. Some time-independent dissipative processes such as brittle damage can also be considered in the same framework. Our attention is focussed on the description of the constitutive equations, on the formulation of the governing equations in terms of the energy potential and the dissipation potential of the solid. A time-discretization by the implicit scheme of the evolution equation leads to the study of the incremental problem which is different from the rate problem. The increment of the response under an increment of the loads must satisfy a variational inequality and, if the energy potential is convex, an incremental minimum principle. In particular, a local minimum of the incremental minimum principle is a stable solution to the variational inequality.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2016.01.004
Mots clés : Gradient plasticity, Brittle damage, Standard models, Evolution equation, Implicit scheme, Incremental problem, Variational principles
Quoc-Son Nguyen 1

1 Laboratoire de Mécanique des Solides, École Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau, France 
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Quoc-Son Nguyen. Quasi-static response, implicit scheme and incremental problem in gradient plasticity. Comptes Rendus. Mécanique, Volume 344 (2016) no. 6, pp. 439-447. doi : 10.1016/j.crme.2016.01.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.01.004/

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