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Shell Theories Arising as low Energy $\Gamma$-Limit of 3D Nonlinear Elasticity
Marta Lewicka, Maria Giovanna Mora and Mohammed Reza Pakzad
We discuss the limiting behavior (using the notion of $\Gamma$-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like $h^4$, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Kármán theory for plates.