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.

刚性/塑性解在某些表面附近是奇异的。解决此类边值问题需要特殊的数值方法。本文为两种压力相关塑性模型开发了这种方法。两者均基于莫尔-库仑屈服准则。考虑静止平面流。数值方法是基于特征的。其显着特点是采用扩展的R-S方法。除了应力场和速度场之外，数值解的输出是应变率强度因子，它控制奇异表面附近的剪切应变率的大小。该方法适用于寻找颗粒材料通过楔形模具流动的解决方案。通过与无限通道流动的解析解和压力无关材料的可用数值解进行比较，验证了该解的准确性。这项研究的一个应用方面是，应变率强度因子可用于非传统本构方程，以预测高摩擦表面附近材料性能的演变。