In this paper we investigate the equivalence of the sequential weak lower semicontinuity of the total energy functional and the quasiconvexity of the stored energy function of the nonlinear micropolar elasticity. Based on techniques of Acerbi and Fusco [Arch. Rational Mech. Anal. 86 (1984) 125-145] we extend the result from Tambača and Velčić [ESAIM: COCV (2008) DOI: 10.1051/cocv:2008065] for energies that satisfy the growth of order p ≥ 1. This result is the main step towards the general existence theorem for the nonlinear micropolar elasticity.
Mots-clés : micropolar elasticity, existence theorem, quasiconvexity, semicontinuity
@article{COCV_2010__16_2_337_0,
author = {Tamba\v{c}a, Josip and Vel\v{c}i\'c, Igor},
title = {Semicontinuity theorem in the micropolar elasticity},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {337--355},
publisher = {EDP-Sciences},
volume = {16},
number = {2},
year = {2010},
doi = {10.1051/cocv/2009002},
mrnumber = {2654197},
zbl = {1193.74007},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2009002/}
}
TY - JOUR AU - Tambača, Josip AU - Velčić, Igor TI - Semicontinuity theorem in the micropolar elasticity JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 337 EP - 355 VL - 16 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2009002/ DO - 10.1051/cocv/2009002 LA - en ID - COCV_2010__16_2_337_0 ER -
%0 Journal Article %A Tambača, Josip %A Velčić, Igor %T Semicontinuity theorem in the micropolar elasticity %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 337-355 %V 16 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2009002/ %R 10.1051/cocv/2009002 %G en %F COCV_2010__16_2_337_0
Tambača, Josip; Velčić, Igor. Semicontinuity theorem in the micropolar elasticity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 2, pp. 337-355. doi : 10.1051/cocv/2009002. http://www.numdam.org/articles/10.1051/cocv/2009002/
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