On the anisotropy of cracked solids

Abstract

We consider the effective elastic properties of cracked solids, and verify the hypothesis that the effect of crack interactions on the overall anisotropy – its type and orientation – is negligible (even though the effect on the overall elastic constants may be strong), provided crack centers are located randomly. This hypothesis is confirmed by computational studies on large number of 2-D crack arrays of high crack density (up to 0.8) that are realizations of several orientation distributions. Therefore, the anisotropy can be accurately determined analytically in the non-interaction approximation (NIA). Since the effective elastic properties possess the orthotropic symmetry in the NIA (for any orientation distribution of cracks, including cases when, geometrically, the crack orientation pattern does not have this symmetry), the orthotropy of cracked solids is not affected by interactions.