We reconsider the derivation of plate theories as -limits of -dimensional nonlinear elasticity and define a suitable notion for the interpenetration of matter in the limit configuration. This is done via the Brouwer degree. For the approximating maps, we adopt as definition of interpenetration of matter the notion of non-invertibility almost everywhere, see [J.M. Ball, Proc. Roy. Soc. Edinburgh Sect. A 88 (1981) 315–328]. Given a limit map satisfying the former interpenetration property, we show that any recovery sequence (in the sense of -convergence) has to consist of maps that satisfy the latter interpenetration property except for finitely many sequence elements. Then we explain how our result is applied in the context of the derivation of plate theories.
Accepté le :
DOI : 10.1051/cocv/2015042
Mots clés : Derivation of plate theories, Γ-convergence, nonlinear plate theory, interpenetration of matter
@article{COCV_2017__23_1_119_0,
author = {Olbermann, Heiner and Runa, Eris},
title = {Interpenetration of matter in plate theories obtained as $\Gamma{}$-limits},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {119--136},
publisher = {EDP-Sciences},
volume = {23},
number = {1},
year = {2017},
doi = {10.1051/cocv/2015042},
mrnumber = {3601018},
zbl = {1364.49015},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2015042/}
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AU - Olbermann, Heiner
AU - Runa, Eris
TI - Interpenetration of matter in plate theories obtained as $\Gamma{}$-limits
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2017
SP - 119
EP - 136
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PB - EDP-Sciences
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DO - 10.1051/cocv/2015042
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Olbermann, Heiner; Runa, Eris. Interpenetration of matter in plate theories obtained as $\Gamma{}$-limits. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 119-136. doi : 10.1051/cocv/2015042. http://www.numdam.org/articles/10.1051/cocv/2015042/
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