Linearized plastic plate models as Gamma-limits of 3D finite elastoplasticity

Abstract

The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of {\Gamma}-convergence, in the framework of finite plasticity. Denoting by {\epsilon} the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy is of order {\epsilon}^(2{\alpha}-2), with {\alpha}>=3. According to the value of {\alpha}, partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von Karman plate theory and the linearized plate theory.