Existence for dislocation-free finite plasticity
ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 21.

This note addresses finite plasticity under the constraint that plastic deformations are compatible. In this case, the total elastoplastic deformation of the medium is decomposed as y = ye ○ yp, where the plastic deformation yp is defined on the fixed reference configuration and the elastic deformation ye is a mapping from the varying intermediate configuration yp(Ω). Correspondingly, the energy of the medium features both Lagrangian (plastic, loads) and not Lagrangian contributions (elastic).

We present a variational formulation of the static elastoplastic problem in this setting and show that a solution is attained in a suitable class of admissible deformations. Possible extensions of the result, especially in the direction of quasistatic evolutions, are also discussed.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2018014
Classification : 35K90
Mots-clés : Finite plasticity, static problem, existence, quasistatic evolution
Stefanelli, Ulisse 1

1 
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Stefanelli, Ulisse. Existence for dislocation-free finite plasticity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 21. doi : 10.1051/cocv/2018014. http://www.numdam.org/articles/10.1051/cocv/2018014/

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