Calculus of Variations and Geometric Measure Theory

M. Buzancic - E. Davoli - I. Velčić

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

created by davoli on 01 Mar 2023


Submitted Paper

Inserted: 1 mar 2023
Last Updated: 1 mar 2023

Year: 2023


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.

Keywords: Gamma-convergence, dimension reduction, quasistatic evolution, rate-independent processes, periodic homogenization, perfect plasticity