Rigorous derivation of a plate theory in linear elastoplasticity via [Gamma]-convergence

Abstract

This paper deals with dimension reduction in linearized elastoplasticity in the rate-independent case. The reference configuration of the elastoplastic body is given by a two-dimensional middle surface and a small but positive thickness. We derive a limiting model for the case in which the thickness of the plate tends to 0. This model contains membrane and plate deformations which are coupled via plastic strains. The convergence analysis is based on an abstract Gamma convergence theory for rate-independent evolution formulated in the framework of energetic solutions. This concept is based on an energy-storage functional and a dissipation functional, such that the notion of solution is phrased in terms of a stability condition and an energy balance.