The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of Γ-convergence, in the framework of finite plasticity. Denoting by ε the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order ε2α-2, with α ≥ 3. According to the value of α, partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von Kármán plate theory and the linearized plate theory.
Mots-clés : finite plasticity, thin plates, Γ-convergence
@article{COCV_2014__20_3_725_0,
author = {Davoli, Elisa},
title = {Linearized plastic plate models as $\Gamma $-limits of {3D} finite elastoplasticity},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {725--747},
publisher = {EDP-Sciences},
volume = {20},
number = {3},
year = {2014},
doi = {10.1051/cocv/2013081},
zbl = {1298.74145},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2013081/}
}
TY - JOUR AU - Davoli, Elisa TI - Linearized plastic plate models as $\Gamma $-limits of 3D finite elastoplasticity JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 725 EP - 747 VL - 20 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2013081/ DO - 10.1051/cocv/2013081 LA - en ID - COCV_2014__20_3_725_0 ER -
%0 Journal Article %A Davoli, Elisa %T Linearized plastic plate models as $\Gamma $-limits of 3D finite elastoplasticity %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 725-747 %V 20 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2013081/ %R 10.1051/cocv/2013081 %G en %F COCV_2014__20_3_725_0
Davoli, Elisa. Linearized plastic plate models as $\Gamma $-limits of 3D finite elastoplasticity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 3, pp. 725-747. doi : 10.1051/cocv/2013081. http://www.numdam.org/articles/10.1051/cocv/2013081/
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