# Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure: the limiting regimes

## TL;DR

This paper derives effective quasistatic evolution models for thin, perfectly plastic plates with periodic microstructure, analyzing different regimes of scale separation using advanced homogenization and dimension reduction techniques.

## Contribution

It introduces a rigorous framework for modeling the behavior of microstructured plastic plates under different scale regimes, combining homogenization and dimension reduction methods.

## Key findings

- Convergence of quasistatic evolutions in different scale regimes
- Effective models capturing microstructure effects
- Application of two-scale convergence and $ ext{Γ}$-convergence techniques

## Abstract

We identify effective models for thin, linearly elastic and perfectly plastic plates exhibiting a microstructure resulting from the periodic alternation of two elastoplastic phases. We study here both the case in which the thickness of the plate converges to zero on a much faster scale than the periodicity parameter and the opposite scenario in which homogenization occurs on a much finer scale than dimension reduction. After performing a static analysis of the problem, we show convergence of the corresponding quasistatic evolutions. The methodology relies on two-scale convergence and periodic unfolding, combined with suitable measure-disintegration results and evolutionary $\Gamma$-convergence.