DIFFERENCE BETWEEN LATTICE AND CONTINUUM FAILURE THRESHOLD IN PERCOLATION

A scaling analysis introduced by Halperin, Feng and Sen to estimate critical exponents for the electrical conductivity and elastic constant is extended to determine the critical behavior of electrical and mechanical failure near the percolation threshold for a class of disordered continuum systems (Swiss-cheese models). Above the dimension d//c equals 3/2 for the electrical problem and at any dimension for the mechanical case, the exponents are significantly larger than their counterpart in the discrete lattice percolation network. The effect is more pronounced than for transport properties due to the extreme brittleness of the weakest bonds.