A viscoplastic approach to model the flow of granular solids

The ¯ow of granular solids within rigid walls is modeled using continuum mechanics. The problem is represented as a viscoplastic ¯ow in which the discontinuity function is taken as in previous works by Gray and Stiles, while the ¯ow rule is modeled by the von-Mises criterion. The resulting model is incompressible and based on non-associated viscoplasticity. The apparent viscosity results in a non-linear function of the second invariant of the symmetric rate of deformation tensor and of the pressure. Friction, cohesion and ¯uidity of the granular model are taken into account. The constitutive model has been implemented assuming steady-state, in which the granular material ¯ows under a critical state (incompressible behavior). Discretization of the problem has been carried out by ®nite elements, with direct iteration techniques to solve the non-linear system of equations. The model has been applied to the massive ¯ow of granular material stored in vertical silos and hoppers with axisymmetric or planar shape. Comparisons with experimental tests performed by other authors are presented, together with parametric investigations to identify the main variables a€ecting the response. #