Fracture of model gel networks under applied strain

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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 a two stage process. First, the random removal of bonds connecting nodes at least one of which has a connectivity greater than a prescribed maximum value. Then the random removal of bonds to obtain any desired value of the mean node connectivity. The fracture of such a network under an incrementally applied uniaxial strain is studied by including a maximum value, L b, for the extension of any spring before irreversible breakage. Random networks with maximally fourfold and maximally threefold connected nodes show qualitatively similar stress-strain curves, but quantitatively differ even when the mean node connectivities of the networks are the same. For sufficiently large L b, the maximum value of the tension is linearly proportional to L b for random networks with either maximally fourfold or maximally threefold connected nodes.