Stiffness Percolation in Stochastically Fragmented Continua

Abstract

We study the mechanical behavior of three-dimensional, randomly microcracked continua for crack densities up to and above the transport percolation threshold. We show the existence of a fully fragmented material state in which stiffness is preserved due to topological interlocking of fragments. In this regime, the mechanical behavior is controlled by the contacts between fragments and becomes nonlinear. The upper limit of crack densities for which this behavior is observed, the stiffness percolation threshold, is identified. The variation of the effective material stiffness for crack densities ranging from 0 to the stiffness percolation threshold is reported.