Calculus of Variations and Geometric Measure Theory

M. Lewicka - M. G. Mora - M. R. Pakzad

Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity

created by mora on 04 Mar 2008
modified on 13 Sep 2010


Published Paper

Inserted: 4 mar 2008
Last Updated: 13 sep 2010

Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci.
Volume: 9
Pages: 253-295
Year: 2010


We discuss the limiting behavior (using the notion of Gamma-limit) of the three-dimensional nonlinear elasticity for thin shells around an arbitrary smooth two-dimensional 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 Kármán theory for plates.

Keywords: Gamma-convergence, dimension reduction, nonlinear elasticity, shell theories