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Shell theories arising as low energy \(\Gamma \)-limit of 3d nonlinear elasticity. (English) Zbl 1425.74298
Summary: 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.

MSC:
74K25 Shells
74B20 Nonlinear elasticity
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