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A nonlinear dynamical system model that approximates a microscopic Gibbsfield model for the yielding of a viscoplastic material subjected to varyingexternal stress recently reported in [1] is presented. The predictions of themodel are in a fair agreement with the microscopic simulations and in a verygood agreement with the microstructural semi-empirical model reported in [2].With only two internal parameters, the nonlinear dynamical system modelcaptures several key features of the solid-fluid transition observed inexperiments: the effect of the interactions between microscopic constituents onthe yield point, the abruptness of solid-fluid transition and the emergence ofa hysteresis of the micro-structural states upon increasing/decreasing externalforcing.The scaling behaviour of the magnitude of the hysteresis with thedegree of the steadiness of the flow is consistent with previous experimentalobservations.

A nonlinear dynamical system approach for the yielding behaviour of a viscoplastic fluid