Effective Elastic Moduli in Solids with High Crack Density

TL;DR

This paper studies how high crack densities weaken elastic solids, comparing numerical results with homogenization theories, and deriving analytical predictions for different crack orientations.

Contribution

It provides new analytical and numerical insights into the effective elastic moduli of cracked solids, especially at high crack densities and specific crack alignments.

Findings

Good agreement with homogenization theories at low crack densities

Material weaker than predictions at high crack densities due to percolation effects

Power law decay of elastic constants for parallel cracks at high densities

Abstract

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.