New solutions for effective elastic moduli of microcracked solids

A new energy balance equation is proposed to evaluate the e€ective moduli of solids with randomly dispersed cracks. In this study, it is assumed that the potential energy released by embedding a circular or spherical RVE with microcracks into an in®nite matrix is equal to that induced by introducing its e€ective medium into the identical in®nite matrix. New non-interacting and self-consistent solutions for the e€ective moduli of linear elastic isotropic solids with randomly oriented microcracks were evaluated on the basis of the present energy balance equation. The linearization of the two present solutions leads to the dilute solution in the limit of small crack density. Comparison studies with various existing solutions are also presented in detail.