We investigate quasistatic evolution in finite plasticity under the assumption that the plastic strain is compatible. This assumption is well-suited to describe the special case of dislocation-free plasticity and entails that the plastic strain is the gradient of a plastic deformation map. The total deformation can be then seen as the composition of a plastic and an elastic deformation. This opens the way to an existence theory for the quasistatic evolution problem featuring both Lagrangian and Eulerian variables. A remarkable trait of the result is that it does not require second-order gradients.
Mots-clés : Elasticity, plasticity, quasistatic evolution
@article{COCV_2020__26_1_A123_0,
author = {Kru\v{z}{\'\i}k, Martin and Melching, David and Stefanelli, Ulisse},
title = {Quasistatic evolution for dislocation-free finite plasticity},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2020031},
mrnumber = {4188823},
zbl = {1465.35373},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2020031/}
}
TY - JOUR AU - Kružík, Martin AU - Melching, David AU - Stefanelli, Ulisse TI - Quasistatic evolution for dislocation-free finite plasticity JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2020031/ DO - 10.1051/cocv/2020031 LA - en ID - COCV_2020__26_1_A123_0 ER -
%0 Journal Article %A Kružík, Martin %A Melching, David %A Stefanelli, Ulisse %T Quasistatic evolution for dislocation-free finite plasticity %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2020031/ %R 10.1051/cocv/2020031 %G en %F COCV_2020__26_1_A123_0
Kružík, Martin; Melching, David; Stefanelli, Ulisse. Quasistatic evolution for dislocation-free finite plasticity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 123. doi : 10.1051/cocv/2020031. http://www.numdam.org/articles/10.1051/cocv/2020031/
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