Discrete Element Methods

Springer Tracts in Mechanical Engineering

Smolin

Dimaki

et al. 2020

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.

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

Springer Tracts in Mechanical Engineering

Smolin

Dimaki

et al. 2020

Role of Adhesion Stress in Controlling Transition between Plastic, Grinding and Breakaway Regimes of Adhesive Wear

Dimaki

Dudkin

et al. 2020

Sci Rep

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.Adhesive wear is a complex, multiscale and still poorly understood phenomenon 1-3 . This kind of wear occurs in contact pairs where materials of interacting bodies are characterized by equal or similar values of hardness with the possible transfer of material from one surface to the opposite one. Since the publication of Rabinowicz from 1958 4 , it is known that adhesive wear is controlled by the relation of material parameters including elastic modulus, hardness and specific surface energy 4,5 . In a series of recent works by Aghababaei, Molinari et al., it was shown that adhesive wear may develop in two ways: 1) formation and evolution (growth or fragmentation) of wear particles or 2) plastic deformation of micro contacts accompanied by smoothing of asperities 6,7 . These studies together with works by other research groups 8-11 created a solid basis for a theoretical understanding of wear modes and opened possibilities for a new interpretation of classical concepts. In particular, the adhesive wear mode criterion by Rabinowicz was critically revised and details were disclosed of how the wear process occurs in both regimes of debris formation and plastic smoothing.The above mentioned fundamental results revealing the features of asperity fracture and wear were obtained using pseudo molecular dynamics (MD) simulation at the mesoscale, so the question remained whether these conclusions are universal and applicable to real materials. A particular problem of meso MD models consists in the difficulty of separating the plastic and adhesive properties of material as in meso molecular dynamics both of them are determined by the same interaction potential. On the mesoscopic scale, it may be necessary, firstly, to decouple strength from adhesion parameters of the material and, secondly to take into account more complex material properties such as yield stress and strain hardening, both strongly dependent on features of internal structure at lower scales (grain structure, grain boundaries, inclusions of other phases, etc.). This substantiates the need for a detailed theoretical analysis of wear r...

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

Konovalenko

2021

Materials

It is well-known that the effect of interstitial fluid on the fracture pattern and strength of saturated high-strength concrete is determined by qualitatively different mechanisms at quasi-static and high strain rate loading. This paper shows that the intermediate range of strain rates (10−4 s−1 < ε˙ < 100 s−1) is also characterized by the presence of a peculiar mechanism of interstitial water effect on the concrete fracture and compressive strength. Using computer simulations, we have shown that such a mechanism is the competition of two oppositely directed processes: deformation of the pore space, which leads to an increase in pore pressure; and pore fluid flow. The balance of these processes can be effectively characterized by the Darcy number, which generalizes the notion of strain rate to fluid-saturated material. We have found that the dependence of the compressive strength of high-strength concrete on the Darcy number is a decreasing sigmoid function. The parameters of this function are determined by both low-scale (capillary) and large-scale (microscopic) pore subsystems in a concrete matrix. The capillary pore network determines the phenomenon of strain-rate sensitivity of fluid-saturated concrete and logistic form of the dependence of compressive strength on strain rate. Microporosity controls the actual boundary of the quasi-static loading regime for fluid-saturated samples and determines localized fracture patterns. The results of the study are relevant to the design of special-purpose concretes, as well as the assessment of the limits of safe impacts on concrete structural elements.