The material point method in the analysis of the problem of shear bounds formation

Publisher Summary This chapter analyzes the problem of mesh sensitivity of the material point solution to granular flow in a silo for the elastic–perfectly plastic material model. It also analyzes the dynamic, large strain problem of shear bounds formation. The material point method is an arbitrary Lagrangian-Eulerian formulation of the finite element method. The method can be classified as a meshless method; it is a well-known method in fluid mechanics as the particle-in-cell method. This chapter investigates the mesh dependence of the numerical solution, obtained by the material point method in the case of elastic-perfectly plastic material model. The mesh independent solution can be found by the use of the viscoplastic regularization of the elastic-plastic constitutive relations. In this case, the thickness of obtained shear bounds depends on the value of viscosity parameter. Boundary-value and initial-boundary-value problems formulated for material models—such as elastic—perfectly plastic model or models with softening—are characterized by nonuniqueness of their solution. The lack of solution uniqueness leads to mesh sensitivity of an approximate solution when the finite element method is employed in the analysis of the problem.