Node coordination constraints and the elasticity of random central force networks

Abstract

Random central force networks are constructed by relaxation of a bond-depleted lattice of Hooke's law springs under tension. The bond depletion procedure involves the random removal of the bonds connecting the nodes of a simple cubic lattice subject to constraints on the coordination of individual nodes. In one model, the random network, random bond depletion is only restricted by the requirement that no node have coordination greater than fourfold. In a second model, the continuous random network, random bond depletion is subject to the additional constraint that the individual node coordination remains at least twofold, thus precluding the formation of any dangling bonds. The elastic properties of the two types of network markedly differ only for small values of the mean node coordination, when the random network contains significantly higher fractions of threefold- and fourfold-coordinated nodes than the continuous random network.