The fracture strength of solids near the percolation threshold

Abstract

The authors develop a relation for the fracture strength of a porous solid or random network near the percolation threshold. Near the percolation threshold the fracture strength vanishes as (p-p_c)^{( tau +v(2-d))}2/, where tau and v are the elasticity and coherence length exponent respectively and d is the fractal dimension of the percolating cluster. Employing this relation, they have determined the elasticity exponent in a recent molecular dynamic investigation to be approximately=2.