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 we identify two different asymptotic theories, depending on the ratio of h and . In the case of convex shells we obtain a complete picture in the whole regime .
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Peter Hornung, Igor Velčić, Derivation of a homogenized von-Kármán shell theory from 3D elasticity. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 5, pp. 1039–1070DOI 10.1016/J.ANIHPC.2014.05.003