A Lagrangian PFEM approach for non-Newtonian viscoplastic materials

Abstract

This paper presents the application of a stabilized mixed Particle Finite Element Method (PFEM) to the solution of viscoplastic non-Newtonian flows. The application of the proposed model to the deformation of granular non-cohesive material is analysed. A variable yield threshold modified Bingham model is presented, using a Mohr Coulomb resistance criterion.

Since the granular material is expected to undergo severe deformation, a Lagrangian approach is preferred to a fixed mesh one. PFEM is the adopted technique.

The detail of the discretization procedure is presented and the Algebraic Sub-Grid Scale (ASGS) stabilization technique is introduced to allow for the use of equal order interpolations for velocity and pressure in a consistent way. The matrix form of the problem is given.

Finally, the differences between the regularized Bingham and the variable yield models are discussed in some examples.