BOUNDS ON THE EFFECTIVE MODULI OF CRACKED MATERIALS

We find bounds on the effective elastic moduli of cracked materials in terms of the effective conductivity of such media. These represent th e first non-trivial bounds on the effective properties of cracked medi a which are independent of the shapes and spatial distribution of the cracks. Different approximations for the elastic moduli of cracked med ia are tested against our bounds. The microgeometries of cracks that s atisfy the bounds exactly are identified.