Elastic properties of three-dimensional percolation networks with stretching and bond-bending forces

We report the results of the first numerical simulations of elastic properties of three-dimensional percolation networks in which both central and bond-bending forces are present. Using extensive Monte Carlo simulations and finite-size scaling analysis and taking into account corrections to scaling, we find $f\simeq 3.78$ with an error of about 3%, where $f$ is the critical exponent that characterizes the power-law behavior of the elastic moduli near the percolation threshold $P_c$. This agrees excellently with the experimental measurements of $f$ for sintered materials and for gels near the gelation point. It also agrees with the relation $f=t+2v$, where $t$ is the critical exponent of the electrical conductivity of the network, and $v$ the correlation-length exponent. Also studied is the ratio of the bulk and shear modulus of the system. As $P_c$ is approached, this ratio approaches a value close to 4/3.