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Effective elastic moduli in solids with high density of cracks

R. Spatschek, C. Gugenberger, E. A. Brener.

Physical Review B, The American Physical Society, 80, 144106, 1-8, (2009)

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.

Keyword(s): cracks, elastic moduli
DOI: 10.1103/PhysRevB.80.144106
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