The boundary-layer method in the fracture mechanics of composites of periodic structure (Q1180870)

The problem of a rectilinear crack in a composite material of doubly- periodic structure is considered. It is assumed that the dimensions of the crack are considerably greater than the cell of material periodicity. A boundary-layer method based on the use of the asymptotic method of averaging periodic structures, taking additional solutions of boundary- layer type [\textit{N. S. Bakhvalov} and \textit{G. P. Panasenko}, Averaging processes in periodic media (1984; Zbl 0607.73009)] into account to allow the edge effect that occurs near the boundary of the crack outline to be considered, is proposed for analysing the stress field in the neighbourhood of a macrocrack.