  The introduced notion of locally-periodic two-scale convergence allows to
average a wider range of microstructures, compared to the periodic one. The
compactness theorem for the locally-periodic two-scale convergence and the
characterisation of the limit for a sequence bounded in $H^1(\Omega)$ are
proven. The underlying analysis comprises the approximation of functions, which
periodicity with respect to the fast variable depends 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.
