Self-consistent elastic moduli of a cracked solid

A self‐consistent theory for the determination of elastic moduli of cracked solids is presented, and worked out for an isotropic distribution of cracks. A missing ingredient of the previous theory of O'Connell and Budiansky is the correct accounting of crack interaction energy. The new theory leads to a set of differential equations for the effective elastic moduli which are easily solved. The solutions always lie within the physical range, and show that the influence of the cracks on the effective moduli is considerably less than has been previously calculated.