Inserted: 1 mar 2023
Last Updated: 1 mar 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