We investigate the weakening of elastic materials through randomly distributed circles and cracks numerically and compare the results to predictions from homogenization theories. We find a good agreement for the case of randomly oriented cracks of equal length in an isotropic plane-strain medium for lower crack densities; for higher densities the material is weaker than predicted due to precursors of percolation. For a parallel alignment of cracks, where percolation does not occur, we analytically predict a power-law decay of the effective elastic constants for high crack densities, and confirm this result numerically.

• Received 15 July 2009

DOI:https://doi.org/10.1103/PhysRevB.80.144106