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

TL;DR

This paper rigorously derives simplified models for thin elastoplastic plates using Gamma-convergence, revealing how different linearizations emerge depending on the energy scaling parameter.

Contribution

It provides a mathematical derivation of reduced elastoplastic plate models as Gamma-limits, connecting nonlinear 3D models to classical plate theories.

Findings

Derivation of linearized plate models from 3D elastoplasticity

Identification of energy scaling regimes leading to different models

Connection between nonlinear and classical linear plate theories

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.