Green’s functions for the periodic four-phase elastic space with an interface crack or a linear rigid inclusion

We construct fundamental solutions of the problem of antiplane deformation of an unbounded composite body with interface cut or a linear rigid inclusion subjected to the action of concentrated forces. The periodic cell of the composite contains four different elements with rectangular cross sections. The problem is studied by the method of homogenization with microlocal parameters. The formulas for the stress intensity factors are obtained in the analytic form and investigated. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 2, pp. 25–32, March–April, 2007.