Fracture of model gel networks

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Abstract
A random central force network model of a gel is constructed by relaxation of a bond diluted simple cubic lattice of Hooke's law springs under tension. The bond dilution procedure, which defines the model, involves the random removal of bonds connecting nodes, at least one of which has a value greater than a prescribed maximum value. The fracture of such a network is studied by including a maximum value, L b, for the extension of any spring before irreversible breakage. The structure and elastic properties of networks with either fourfold or threefold maximum node connectivity are calculated as a function of the model parameter L b. The model with maximally fourfold connected nodes shows a fracture instability for values of L b less than a well-defined critical value in sufficiently large systems, the structural failure of the system being associated with a loss of fourfold connected nodes. Models with maximally threefold connected nodes do not show any critical value of L b for fracture instability over the physically allowed range of L b values.