Two-scale convergence for locally-periodic microstructures and homogenization of plywood structures

摘要

The introduced notion of locally-periodic two-scale convergence allows toaverage a wider range of microstructures, compared to the periodic one. Thecompactness theorem for the locally-periodic two-scale convergence and thecharacterisation of the limit for a sequence bounded in $H^1(\Omega)$ areproven. The underlying analysis comprises the approximation of functions, whichperiodicity with respect to the fast variable depends on the slow variable, bylocally-periodic functions, periodic in subdomains smaller than the considereddomain, but larger than the size of microscopic structures. The developedtheory is applied to derive macroscopic equations for a linear elasticityproblem defined in domains with plywood structures.