A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret (1995). Specific characterizations of the 2D elastic energy are produced. As a generalization of Bouchitté et al. (2002), the case where external loads induce a density of bending moment that produces a Cosserat vector field is also investigated. Throughout, the 3D-2D dimensional reduction is viewed as a problem of -convergence of the elastic energy, as the thickness tends to zero.
Keywords: dimension reduction, $\Gamma $-convergence, equi-integrability, quasiconvexity, relaxation
@article{COCV_2005__11_1_139_0,
author = {Babadjian, Jean-Fran\c{c}ois and Francfort, Gilles A.},
title = {Spatial heterogeneity in {3D-2D} dimensional reduction},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {139--160},
year = {2005},
publisher = {EDP Sciences},
volume = {11},
number = {1},
doi = {10.1051/cocv:2004031},
mrnumber = {2110618},
zbl = {1085.49015},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv:2004031/}
}
TY - JOUR AU - Babadjian, Jean-François AU - Francfort, Gilles A. TI - Spatial heterogeneity in 3D-2D dimensional reduction JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2005 SP - 139 EP - 160 VL - 11 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv:2004031/ DO - 10.1051/cocv:2004031 LA - en ID - COCV_2005__11_1_139_0 ER -
%0 Journal Article %A Babadjian, Jean-François %A Francfort, Gilles A. %T Spatial heterogeneity in 3D-2D dimensional reduction %J ESAIM: Control, Optimisation and Calculus of Variations %D 2005 %P 139-160 %V 11 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv:2004031/ %R 10.1051/cocv:2004031 %G en %F COCV_2005__11_1_139_0
Babadjian, Jean-François; Francfort, Gilles A. Spatial heterogeneity in 3D-2D dimensional reduction. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 139-160. doi: 10.1051/cocv:2004031
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