Particle-Based Approach for Simulation of Nonlinear Material Behavior in Contact Zones

Abstract

Methods of particles are now recognized as an effective tool for numerical modeling of dynamic mechanical and coupled processes in solids and liquids. This chapter is devoted to a brief review of recent advances in the development of the popular particle-based discrete element method (DEM). DEM is conventionally considered as a highly specialized technique for modeling the flow of granular media and the fracture of brittle materials at micro- and mesoscopic scales. However, in the last decade, great progress has been made in the development of the formalism of this method. It is largely associated with the works of the scientific group of Professor S. G. Psakhie. The most important achievement of this group is a generalized formulation of the method of homogeneously deformable discrete elements. In the chapter, we describe keystones of this implementation of DEM and a universal approach that allows one to apply various rheological models of materials (including coupled models of porous fluid-saturated solids) to a discrete element. The new formalism makes possible qualitative expansion of the scope of application of the particle-based discrete element technique to materials with various rheological properties and to the range of considered scales form microscopic to macroscopic. The capabilities of this method are especially in demand in the study of the features of contact interaction of materials. To demonstrate these capabilities, we briefly review two recent applications concerning (a) the effect of adhesive interaction on the regime of wear of surface asperities under tangential contact of bodies and (b) the nonmonotonic dependence of the stress concentration in the neck of the human femur on the dynamics of hip joint contact loading.

Numerical Modeling of Shockwave Treatment of Knee Joint

“…To describe the mechanical behavior of biological tissues, herein we used the model of a poroelastic body, implemented in the method of movable cellular automata (MCA) [30,31], which is an efficient method of computational particle (discrete) mechanics. It has been established that discrete methods have proven themselves to be very promising for modeling contact loading of different materials at both the macroscale and the mesoscale [32,33]. In the MCA method, a solid is considered as an ensemble of discrete elements of finite size (cellular automata) that interact with each other according to certain rules, which, within the particle approach, and due to many body interaction forces, describe the deformation behavior of the material as an isotropic elastoplastic body.…”

Nonlinear Mechanical Effect of Free Water on the Dynamic Compressive Strength and Fracture of High-Strength Concrete

“…The mechanical behavior of the model concrete samples under loading was modeled using the method of homogeneously (simply) deformable discrete elements [ 62 , 74 ]. The discrete element method (DEM) is based on the representation of a material as an ensemble of interacting (chemically bonded or contacting) particles with a given mass, shape, volume, and surface area [ 75 , 76 ].…”

“…Within the framework of this method, stresses and strains in the volume of an element are assumed to be uniformly distributed and characterized by tensors of averaged stresses and strains. The components of the average stress tensor in the discrete element i are calculated as a superposition of the forces of interaction of the element with its neighbors [ 62 , 74 ] (Equation (3)): where R i is the radius of equivalent disk/ball, is the initial value of the contact area of the element i with the neighbor j (contact square for unstrained pair), is the volume of the unstrained element i , α,β = x , y , z ( XYZ is laboratory coordinate system), cosθ ij ,α is the projection of the unit normal vector onto the α-axis, and N i is the number of neighbors of the element. The components of the average strain tensor in the discrete element i can be calculated as a superposition of normal and tangential pair strains by analogy with Equation (3) or incrementally with the use of the material’s constitutive law and calculated average stresses.…”

“…Within the framework of this method, stresses and strains in the volume of an element are assumed to be uniformly distributed and characterized by tensors of averaged stresses and strains. The components of the average stress tensor in the discrete element i are calculated as a superposition of the forces of interaction of the element with its neighbors [62,74] (Equation ( 3)):…”

A Discrete Element Formalism for Modelling Wear Particle Formation in Contact Between Sliding Metals

“…The authors of this paper develop the original formulation of DEM, namely, the method of homogeneously deformable discrete elements [34]. This formulation makes it possible to implement models of the mechanical behavior of materials with complex rheological properties (including elastic-plastic) [35], as well as to take into account surface adhesion. Using these models, the basic modes of deformation and fracture of initial mesoscopic asperities were systematically analyzed for the first time and the influence of surface adhesion and macroscopic material properties was generalized [36,37].…”