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

Department of Mathematical Sciences, Carnegie-Mellon University, Pittsburgh, PA 15213, USA
edavoli@andrew.cmu.edu

Received: 27 November 2012
Revised: 15 July 2013

Abstract

The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of Γ-convergence, in the framework of finite plasticity. Denoting by ε the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order ε^2α−2, with α ≥ 3. According to the value of α, partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von Kármán plate theory and the linearized plate theory.