The effective moduli of cracked bodies in plane deformations

Two essentially different methods for the determination of the effective elastic moduli of a cracked body under plane stress or plane strain deformations are given. The cracks are randomly oriented and distributed such that the cracked material is effectively isotropic. Both methods involve the concept that a single crack surrounded by some matrix material "sees" an effective medium. Each method leads to a simultaneous nonlinear system of equations in the unknown overall properties. Results are given for a cracked plate, and the predicted moduli are compared with those of the self-consistent method. The latter approach underestimates the moduli, and yields an unrealistic result of predicting zero stiffnesses at a finite crack density parameter. The presently obtained moduli are higher than those provided by the self-consistent scheme.