We find bounds on the effective elastic moduli of cracked materials in terms of the effective conductivity of such media. These represent the first non-trivial bounds on the effective properties of cracked media which are independent of the shapes and spatial distribution of the cracks. Different approximations for the elastic moduli of cracked media are tested against our bounds. The microgeometries of cracks that satisfy the bounds exactly are identified.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering