Modeling of the differential rotation effect in complex loading of granular media

A plane problem of directed mass transfer in a granular medium, induced by complex loading with continuous rotation of the principal axes of the strain tensor, is considered. It is proposed to use a hypoplastic model of a granular medium and a model of similarity of a viscous incompressible fluid to describe this effect. A finite-element algorithm is developed for the hypoplastic model, and a numerical solution of a boundary-value problem is constructed. An approximate analytical solution of the initial problem is obtained for the model of similarity of a viscous incompressible fluid. Calculations of deformation kinetics are performed for both models, and the results obtained are compared with available experimental data. Both models are demonstrated to ensure a qualitative description of the deformation process and the effect of directed mass transfer observed in experiments.