A discrete-element based model of elastic-plastic materials with non-ideal plasticity and with an account of both cohesive and adhesive interactions inside the material is developed and verified. Based on this model, a detailed study of factors controlling the modes of adhesive wear is performed. Depending on the material and loading parameters, we observed three main modes of wear: slipping, plastic grinding, cleavage, and breakaway. We find that occurrence of a particular mode is determined by the combination of two dimensionless material parameters: (1) the ratio of the adhesive stress to the pure shear strength of the material, and (2) sensitivity parameter of material shear strength to local pressure. The case study map of asperity wear modes in the space of these parameters has been constructed. Results of this study further develop the findings of the widely discussed studies by the groups of J.-F. Molinari and L. Pastewka.

We study the problem of tangential frictional contact in the presence of adhesion. The model can be considered as a generalization of the theory by Cattaneo and Mindlin to the case where there are “long range adhesive interactions” between the contacting surfaces, which exert an additional pressure on the surfaces even in the absence of an external normal force. The adhesion forces are described by the Dugdale model and the tangential forces in the contact by Coulomb’s law of dry friction. These approximations allow obtaining an analytical solution for the tangential contact problem of a rigid parabolic indenter and a half-space. As in the case of nonadhesive contact, application of an arbitrarily small tangential force leads to slip in the narrow ring-shaped area near the contact boundary. Further increase in tangential load leads to a decrease in the radius of the stick region until sliding expands to the entire contact region. The obtained analytical solution shows that the main governing parameter of the problem is the parameter introduced by Maugis for the normal adhesive contact problem.

Recently, Pohrt and Popov have shown that for simulation of adhesive contacts a mesh dependent detachment criterion must be used to obtain the mesh-independent macroscopic behavior of the system. The same principle should be also applicable for the simulation of fracture processes in any method using finite discretization. In particular, in the Discrete Element Methods (DEM) the detachment criterion of particles should depend on the particle size. In the present paper, we analyze how the mesh dependent detachment criterion has to be introduced to guarantee the macroscopic invariance of mechanical behavior of a material. We find that it is possible to formulate the criterion which describes fracture both in tensile and shear experiments correctly.