Elastic properties of solids containing elliptic cracks
Stefano Giordano and Luciano Colombo

We investigate the elastic properties of multi-cracked solids, by considering dispersions of elliptic cracks with arbitrary non-random orientational distributions. We provide a unified theory covering all of the possible orientational distributions, ranging from the totally random one to the distribution where cracks are preferentially oriented in a given direction. We especially focus on the orthorhombic symmetry and transversely isotropic symmetry, for the cracks distribution. In both cases, the elastic behavior is proved to depend upon the density of cracks and upon some order parameters. Finally, the regime of large crack density and isotropic orientation is studied by means of iterated homogenization and it is shown that the effective elastic moduli depend exponentially on the crack density.

© 2008 The American Physical Society.