Quasistatic evolution models for thin plates arising as low energy Gamma-limits of finite plasticity

TL;DR

This paper derives reduced quasistatic evolution models for thin plates in finite plasticity by analyzing the Gamma-convergence of three-dimensional models as the plate thickness approaches zero, revealing how different scalings affect the limit models.

Contribution

It introduces a rigorous derivation of linearized quasistatic evolution models for thin plates from three-dimensional finite plasticity via Gamma-convergence, depending on the scaling parameter.

Findings

Solutions converge to reduced models as thickness tends to zero

Different scalings lead to different limit models

Provides a rigorous mathematical framework for thin plate plasticity

Abstract

In this paper we deduce by {\Gamma}-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by {\epsilon} the thickness of the plate, we study the case where the scaling factor of the elasto- plastic energy is of order {\epsilon}^ (2{\alpha}-2), with {\alpha}>=3. We show that solutions to the three- dimensional quasistatic evolution problems converge, as the thickness of the plate tends to zero, to a quasistatic evolution associated to a suitable reduced model depending on {\alpha}.