An accurate numerical method of solving singular boundary value problems for the stationary flow of granular materials and its application

The rigid/plastic solutions are singular near certain surfaces. A special numerical method is required to solve such boundary value problems. The present paper develops such a method for two models of pressure-dependent plasticity. Both are based on the Mohr–Coulomb yield criterion. Stationary planar flows are considered. The numerical method is characteristics-based. Its distinguishing feature is employing the extended R–S method. The output of numerical solutions, in addition to stress and velocity fields, is the strain rate intensity factor, which controls the magnitude of the shear strain rate near the singular surface. The method applies to finding a solution for the flow of granular material through a wedge-shaped die. The accuracy of the solution is verified by comparison with an analytical solution for the flow through an infinite channel and an available numerical solution for pressure-independent material. An applied aspect of this study is that the strain rate intensity factor can be used in non-traditional constitutive equations for predicting the evolution of material properties near surfaces with high friction. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.