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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. [ABSTRACT FROM AUTHOR]

This paper develops an approach to model the deformation and fracture of heterogeneous materials at different scales (including multiscale modeling) within a discrete representation of the medium. Within this approach, molecular dynamics is used for the atomic-scale simulation. The simply deformable distinct element method is applied for simulating at higher length scales. This approach is proposed to be implemented using a general way to derive relations for interaction forces between distinct elements in a many-body approximation similar to that of the embedded atom method. This makes it possible to overcome limitations of the distinct element method which are related to difficulties in implementing complex rheological and fracture models of solids at different length scales. For an adequate description of the mechanical behavior features of materials at the micro- and mesoscales, two kinds of models that consider grain and phase boundaries within the discrete element framework are proposed. Examples are given to illustrate the application of the developed formalism to the study of the mechanical response (including fracture) of materials with multiscale internal structure. The examples show that the simply deformable distinct element method is a correct and efficient tool for analyzing complex problems in solid mechanics (including mechanics of discontinua) at different scales. [ABSTRACT FROM AUTHOR]

Conventionally discussed dynamic mechanisms of elastic strain energy redistribution in near-contact surface regions include P and S elastic wave pulses radiating from the contact surface. At the same time, the elastic strain energy can be transferred by localized vortex-like elastic waves (Rayleigh, Love, Stoneley wave, and so on). In the paper, we numerically studied the main features of the formation and propagation of localized vortex-like waves in the surface layers under the contact zone. The study was done using the numerical method of movable cellular automata. We showed that the initial phase of dynamic contact interaction with a nonzero tangential component of contact velocity is accompanied by the formation of a so-called elastic vortex. The elastic vortex is a fully dynamic object, which is characterized by shear stress concentration and propagates at the shear wave speed. We first revealed the ability of the elastic vortex to propagate toward the bulk of the material and transfer elastic strain energy deep into the surface layer in a localized manner. We analyzed the dependence of the direction of vortex propagation on the tangential contact velocity, contact pressure and Young’s modulus of the material. The results of the study are important for better understanding the dynamic mechanisms contributing to inelastic strain accumulation or gradual degradation of surface layers. [ABSTRACT FROM AUTHOR]

Highlights • A dynamic formulation of discrete element method based models is developed. • Discontinuity nucleation time is used as a physical parameter instead of strain rate. • An approach to generalize quasi-static models for dynamic problems is proposed. • The proposed approach is applicable to various Lagrangian numerical methods. Abstract The paper presents an approach to developing the mathematical formalism of the discrete element method to numerically study the inelastic behavior and fracture of brittle materials under dynamic loading. The approach adopts the basic principles of the kinetic theory of strength which postulate the finite time of nucleation of discontinuities and relaxation of local stresses in the material. A general methodology is proposed for constructing dynamic (kinetic) models of the mechanical behavior of a discrete element based on quasi-static models and using three dynamic material parameters (time parameters). The physical meaning of these parameters is discussed, and a method is proposed for estimating the magnitude of the parameters for a considered material using standard experimental data on its mechanical characteristics. The approach is verified by a dynamic formulation of two-parameter models of inelasticity and strength of brittle materials within the method of simply deformable discrete elements. The proposed way to the dynamic generalization of conventional quasi-static mechanical models is applicable to various Lagrangian numerical methods and makes it possible to numerically study the dynamic behavior features and to predict the mechanical characteristics of brittle materials at different strain rates (up to strain rates 103 s−1) and different types of stress state. [ABSTRACT FROM AUTHOR]