Anisotropic effective moduli of microcracked materials under antiplane loading

Abstract

This study focuses on the prediction of the anisotropic effective elastic moduli of a solid containing microcracks with an arbitrary degree of alignment by using the generalized self-consistent method (GSCM). The effective elastic moduli pertaining to anti-plane shear deformation are discussed in detail. The undamaged solid can be isotropic as well as anisotropic. When the undamaged solid is isotropic, the GSCM can be realized exactly. When the undamaged solid is anisotropic it is difficult to provide an analytical solution for the crack opening displacement to be used in the GSCM, thus an approximation of the GSCM is pursued in this case. The explicit expressions of coupled nonlinear equations for the unknown effective moduli are obtained. The coupled nonlinear equations are easily solved through iteration.