Percolation properties of granular elastic networks in two dimensions

The percolation properties of two-dimensional rotationally invariant granular random elastic networks (the disk model) are studied by use of both numerical simulations and finite-size scaling analysis. For the case of normal–empty-bond random networks, an exponent f≊3.2±0.4, which governs the behavior of the network elasticity above percolation threshold $p_c$, is found to be the same as the corresponding exponent for the bond-bending force model studied earlier. For the case of rigid–normal-bond networks, a new exponent c≊1.02±0.07 which governs the elasticity below $p_c$ is found, which is close to but smaller than the superconductivity exponent s. These results can be understood qualitatively by use of the nodes-links-blobs picture of percolation backbones and scaling arguments.