On the solution of plane flow of granular media for jump non‐homogeneity

Abstract

AbstractThis paper deals with the plane plastic equilibrium of a cohesive frictional material in the case of a jump non‐homogeneity. Three types of interface separating rigid‐plastic bodies with different material parameters are distinguished: (i) a perfect adhesion contact, (ii) a thin layer of a material different from the adjacent bodies, (iii) a combined frictional‐adhesive contact. A sliding along the interface may occur if certain conditions are satisfied. For the first two types of joint, the direction and propagation of the velocity jump vector along the interface follow from the classical theory of plane plastic flow. In the third case, the potential sliding rule relating the velocity jump vector to the limit condition of the joint, or to the potential different from the limit condition, may be adopted. The direction of the velocity jump vector results from such a rule.The problem of stability of a slope, being continuously non‐homogeneous in one region, and homogeneous in another, is shown in an example. The two regions of the slope are separated by the interface, a thin layer of a different material, (type ii). The associated flow law for both regions of the slope and for the material of the interface is assumed.