Effective elastic moduli of an isotropic medium weakened by identically oriented disk-shaped cracks

A strict approach to the study of effective elastic moduli of an isotropic medium containing a set of flat parallel cracks is proposed. The idea of th e approach is to use a generalized periodic structural model and to reduce model boundary-value problems formulated based on it to a system of linear algebraic equations. Integrating the stress field over a structure cell yie lds exact finite expressions for all the components of the effective elasti city tensor. The numerical results illustrating the effect of the crack arr angement on the effective stiffness of a cracked body are presented and com pared with known approximate theories.