The Plastic Potential, Double-slip, Double-spin and Viscoplasticity

Abstract

In this paper we describe two classical models for rate‐independent behaviour of granular materials, namely the plastic potential and the double shearing model, emphasising their ill‐posedness. We then describe a model, called the doubleslip and double‐spin model which generalises the plastic potential model and is closely related to the double shearing model. This new model eliminates the causes of the ill‐posedness in the classical models and provides a suitable basis for the analysis of the deformation and flow of granular materials in the rate‐independent regime.There has been considerable recent interest in the intermediate regime between densely‐packed, rate‐independent, quasistatic flow and the rate‐dependent dilute gaseous regime. In this intermediate regime the material also exhibits a degree of ratedependence. The natural extension of a rate‐independent plasticity model to incorporate rate‐dependent material behaviour is by way of viscoplasticity. The archetypal example here is the Bingham material which generalises a von Mises type plasticity model and introduces a viscosity parameter into the model. We propose an extension of the double‐slip and double‐spin model to incorporate viscosity, thereby extending the range of the model to incorporate rate‐dependent behaviour. The new model is then applied to a simplified problem of pipe flow.