Justification of elastoplastic plate models

Abstract

Starting with a three-dimensional Hencky model on an open set ω×]−ε,ε[, we give a mathematical justification of two-dimensional elastoplastic plate models. Following the work of Duvaut, Lions and Temam, we use the variational form of elastoplastic problems as the starting point of discussion and we use the theory of Γ-convergence to examine the limiting behaviour of the problem when ε→0. We conclude that the solutions of three-dimensional plate problems converge to those of two-dimensional plate problems under regularity hypotheses on the boundary conditions. Finally, convergence of the limit analysis energy is also verified.