Solid-fluid Transition in Granular Flows: MPM Simulations with a New Constitutive Approach

Many natural phenomena (rock or snow avalanches, and debris flows) as well as industrial processes are characterized by the flow of solid particles. A key issue in the development of a numerical tool for the study of this problem is the implementation of a suitable constitutive model, capable of capturing the complex rheological behaviour of the granular material in a wide range of strain rates. At the micro-scale level, the grains interacts by enduring frictional contacts or by nearly instantaneous collisions. The first mechanism prevails at low shear rates, when the material behaves like a solid (quasi-static conditions); the latter prevails at high shear rates, when it behaves like a fluid or a granular gas (collisional conditions). This paper presents a new constitutive model able to describe the behaviour of granular materials from quasi-static to collisional conditions and the transition in between. The stress tensor is assumed to be the sum of a quasi-static and a collisional contribution: the former one is modelled by adopting an elasto-plastic model incorporating the critical state concept, whereas the latter stems from the kinetic theory of granular gases. The features of the constitutive model are illustrated with a volume element test; moreover the model has been implemented in the MPM code Anura3D and applied to the simulation of triaxial tests.