This paper presents a novel, yet thermodynamically consistent, model of the isothermal compaction of loose granular material based on the principle of maximum dissipation rate. The method is first tested out on a simple version of the Bingham model and a hard particle model of rate-independent granular flow where it is seen that only the dissipation function and dilatancy rule are required in either case and the procedures are identical. This hard particle model is subsequently modified by the introduction of damage. Yield surface and flow rules are produced that are broadly in accordance with experimental findings. The key to the above modification is the concept of a dilatancy rule with two contributions. (1) A shear induced negative dilatancy, where any shear deformation has a tendency to produce densification. (2) Under many circumstances, this is countered by positive dilatancy such as at the critical state where the two mechanisms balance. This modification uses the idea that the first contribution is encouraged by microscopic damage local to the particle contacts that might permit compaction to occur under hydrostatic pressure alone. A mechanism is postulated whereby shear stresses operating at the microscopic level, while cancelling out at the macroscopic level, might occur with low levels of damage but produce no overall shear strains.
- maximum dissipation rate