Strength of disordered solids

Abstract

The response of a bond-diluted elastic network, when it is subjected to an external stress, is discussed. For low-bond-dilution concentration, the statistics of lattice animals can provide a measure of the strength (fracture stress) of such a system and lead to the conventional Weibull form for the flaw distribution function g(s). Near the percolation threshold p_c of the system, we use the "node-link-blob" model of the percolation cluster to study the critical behavior of the strength of such a bond-diluted elastic network. As p→p_c, strength goes to zero with the critical exponent T'. A scaling relation for T' is obtained, which is exact for dimension d=6 and gives a lower bound for d< 6. Agreement of the scaling relation with experimental results are discussed. Finally we present a Monte Carlo renormalization-group (MCRG) study in a very simplistic elastic model in d=2 dimensions, along with a straightforward Monte Carlo simulation (MCS) for the elastic response and strength of the same model system of size 50×50. The elastic exponent T and the fracture exponent T', obtained for the model either from MCRG or from MCS, are in perfect conformity (within the limit of statistical errors) with our scaling relation.