Accepted Paper

Inserted: 1 mar 2023
Last Updated: 29 dec 2023

Journal: Advances in Calculus of Variations
Year: 2023

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.

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

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