From SBD to SBH: The elastic-plastic plate (Q1599061)

A variational model of an elastic-plastic plate with flat unstressed configuration is presented. The model is derived by an asymptotic analysis of a thick elastic body with small mesoscopic cracks. The case of a rigid plastic slab is also analysed. It is shown that the elastic perfectly plastic energy of the plate is a variational limit of the fracture-elastic energy of a three-dimensional body whose thickness goes to zero. The asymptotic behavior of the constant in the Korn-Poincaré inequality for an \(n\)-dimensional cylinder, when its height tends to zero, and the convergence of minimizers to equilibria of the elastic-plastic plate and the safe load condition are analysed. The techniques of the proofs of the convergence results rely on \(\Gamma\) convergence methods.