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 (where h is the thickness of a shell), we derive a limiting theory which is a generalization of the von K\'arm\'an theory for plates.
Categories: math.FA math-ph math.MP