A Griffith interface crack in a micro-periodic reinforced elastic composite

This paper is devoted to the anti-plane static problem of an interface Griffith crack in a micro-periodic composite solid. The repeated unit cell of the body under consideration consists of four different elastic materials taking the shape of the fibers of infinite length with rectangular cross-sections. An approximate analysis is carried out within the homogenized model with microlocal parameters. The analytical results obtained may be used for the interface crack problems in micro-periodic fiber-reinforced composites as well as in solids with layered or chessboard periodic microstructures.