Two-Scale Convergence for Locally Periodic Microstructures and Homogenization of Plywood Structures

Abstract

The introduced notion of locally periodic two-scale convergence allows one to average a wider range of microstructures, compared to the periodic one. The compactness theorem for locally periodic two-scale convergence and the characterization of the limit for a sequence bounded in $H^1(\Omega)$ are proven. The underlying analysis comprises the approximation of functions, with the periodicity with respect to the fast variable being dependent on the slow variable, by locally periodic functions, periodic in subdomains smaller than the considered domain but larger than the size of microscopic structures. The developed theory is applied to derive macroscopic equations for a linear elasticity problem defined in domains with plywood structures.