Elastic moduli of a cracked solid

Calculations on the basis of the self-consistent method are made for the elastic moduli of bodies containing randomly distributed flat cracks, with or without fluid in their interiors. General concepts are outlined for arbitrary cracks and explicit derivations together with numerical results are given for elliptic cracks. Parameters are identified which adapt the elliptic-crack results to arbitrary convex crack shapes. Finally, some geometrical relations involving randomly distributed cracks and their traces on cross-sections are presented.