Derivation of a homogenized von-Kármán shell theory from 3D elasticity
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 5, pp. 1039-1070.

We derive homogenized von Kármán shell theories starting from three dimensional nonlinear elasticity. The original three dimensional model contains two small parameters: the period of oscillation ε of the material properties and the thickness h of the shell. Depending on the asymptotic ratio of these two parameters, we obtain different asymptotic theories. In the case hϵ we identify two different asymptotic theories, depending on the ratio of h and ϵ 2 . In the case of convex shells we obtain a complete picture in the whole regime hϵ.

DOI: 10.1016/j.anihpc.2014.05.003
Keywords: Elasticity, Dimension reduction, Homogenization, Shell theory, Two-scale convergence
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     title = {Derivation of a homogenized {von-K\'arm\'an} shell theory from {3D} elasticity},
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     publisher = {Elsevier},
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Hornung, Peter; Velčić, Igor. Derivation of a homogenized von-Kármán shell theory from 3D elasticity. Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 5, pp. 1039-1070. doi : 10.1016/j.anihpc.2014.05.003. http://archive.numdam.org/articles/10.1016/j.anihpc.2014.05.003/

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