Derivation of a homogenized von-Kármán shell theory from 3D elasticity

Hornung, Peter; Velčić, Igor

Annales de l'I.H.P. Analyse non linéaire, Tome 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 $h\ll ϵ$ 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 $h\ll ϵ$.

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