Continuum Model of Medium with Cracks

A continuum approach to an elastic medium containing cracks is developed. A crack density tensor describing the averaged geometry of a crack array is introduced and used to study the anisotropy of an effective elastic response due to the presence of cracks. The resulting continuum model turns out to be orthotropic, which is in good agreement with the results given by the small concentration approach and the self-consistent method. Anisotropy of the transport properties (fluid permeability, electric- and heat conductivity) is also considered.