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