Dynamic compaction of granular materials

An Eulerian hyperbolic multiphase flow model for dynamic and irreversible compaction of granular materials is constructed. The reversible model is first constructed on the basis of the classical Hertz theory. The irreversible model is then derived in accordance with the following two basic principles. First, the entropy inequality is satisfied by the model. Second, the corresponding 'intergranular stress' coming from elastic energy owing to contact between grains decreases in time (the granular media behave as Maxwell-type materials). The irreversible model admits an equilibrium state corresponding to von Mises-type yield limit. The yield limit depends on the volume fraction of the solid. The sound velocity at the yield surface is smaller than that in the reversible model. The last one is smaller than the sound velocity in the irreversible model. Such an embedded model structure assures a thermodynamically correct formulation of the model of granular materials. The model is validated on quasi-static experiments on loading-unloading cycles. The experimentally observed hysteresis phenomena were numerically confirmed with a good accuracy by the proposed model.