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.
Accepté le :
DOI : 10.1051/cocv/2018014
Keywords: Finite plasticity, static problem, existence, quasistatic evolution
Stefanelli, Ulisse 1
@article{COCV_2019__25__A21_0,
author = {Stefanelli, Ulisse},
title = {Existence for dislocation-free finite plasticity},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2019},
publisher = {EDP Sciences},
volume = {25},
doi = {10.1051/cocv/2018014},
zbl = {1442.35449},
mrnumber = {3982967},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2018014/}
}
TY - JOUR AU - Stefanelli, Ulisse TI - Existence for dislocation-free finite plasticity JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2019 VL - 25 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2018014/ DO - 10.1051/cocv/2018014 LA - en ID - COCV_2019__25__A21_0 ER -
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
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