Elastic moduli near percolation in a two-dimensional random network of rigid and nonrigid bonds

A mixture of rigid and normal elastic links with both a stretching and a bending force constant is simulated on a two-dimensional, random-bond, honeycomb network in order to investigate the critical behavior of the two macroscopic elastic moduli near the percolation threshold of the rigid bonds p=pc. Both moduli are found to diverge as p{→}pc from below with the same critical exponent that characterizes the electrical conductivity of a superconductor--normal-conductor mixture. Poisson's ratio is found to have a universal negative value that is independent of the microscopic force constants.