Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure

TL;DR

This paper develops an effective quasistatic model for thin perfectly plastic plates with periodic microstructure, combining homogenization and dimension reduction techniques to account for microstructural effects.

Contribution

It introduces a novel approach that simultaneously applies homogenization and dimension reduction to model microstructured plastic plates in the quasistatic regime.

Findings

Derived a limiting model via evolutionary $ extGamma$-convergence

Established convergence results using two-scale and periodic unfolding methods

Provided insights into the microstructure's influence on plastic behavior

Abstract

An effective model is identified for thin perfectly plastic plates whose microstructure consists of the periodic assembling of two elastoplastic phases, as the periodicity parameter converges to zero. Assuming that the thickness of the plates and the periodicity of the microstructure are comparably small, a limiting description is obtained in the quasistatic regime via simultaneous homogenization and dimension reduction by means of evolutionary $\Gamma$-convergence, two-scale convergence, and periodic unfolding.