Modeling the behavior of complex media by jointly using discrete and continuum approaches

Abstract

Investigation of the laws governing the behavior of complex media under the action of various external factors is necessary for solving many basic, technological, and engineering problems. An important part in such investigations belongs to methods and approaches developed by computational mechanics. For a long time, most numerical methods were based on the approaches developed within the framework of the mechanics of continuum. It should be noted that application of the methods of continuum mechanics to description of the process of deformation encounters considerable difficulties in the presence of local straining, discontinuities, intense vortex deformations, and agitation of masses. These problems are especially significant in the case of highly porous and heterogeneous materials and composites with strongly different properties of components.Discrete approaches capable of explicitly modeling the processes involving agitation of masses were developed predominantly for the investigation of granulated and friable media [1][2][3][4], in which the basic elements can be modeled by particles. For this reason, most of these investigations use the equations of motion in the form typical of the method of particles [4] and the interaction forces are calculated within the framework of the model of hard or soft spheres. However, this formalism does not provide correct description of the behavior of continuous isotropic media.The numerical method of movable cellular automata (MCA) extensively developed in recent years [5][6][7][8][9] is free of this disadvantage. While using a discrete approach, this method is based on the equations of motion, which are different from classical equations. In particular, it was shown [7] that, when the characteristic automaton size tends to zero, the MCA formalism allows a transition to the relations of continuum mechanics. The main advantage of this method is the possibility of explicitly modeling both the motion of continuous media and the agitation of masses, including the formation of discontinuities of various types (from the generation of individual defects to the main crack propagation). This circumstance for the first time provides prerequisites for jointly using discrete and continuum approaches within the framework of a common computational scheme, thus combining the advantages of both approaches for solving problems related to modeling of complex objects containing explicit zones of intense straining and fracture. This paper is devoted to the joint use of discrete and continuum approaches, which is important for the development of computational mechanics. The new approach is based on two methods successfully used in recent years. The first method, based on the continuum approach, is the finite difference method of solution of the dynamical problems of elastoplastic deformation of continuous media, and the second is the MCA method based on the discrete description.Since both methods employed in the proposed approach are well known [5,6, 10], we will only consider the questions p...

Modeling of nanostructuring burnishing on different scales

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The Fundamental Regularities of the Evolution of Elastic Vortices Generated in the Surface Layers of Solids under Tangential Contact Loading

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Influence of phase interface properties on mechanical characteristics of metal ceramic composites

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