Abstract
A general approach to realization of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of particle-based numerical methods is proposed in the paper. It is based on building many-body forces of particle interaction, which provide response of particle ensemble correctly conforming to the response (including elastic-plastic behavior and fracture) of simulated solids. Implementation of proposed approach within particle-based methods is demonstrated by the example of the movable cellular automaton (MCA) method, which integrates the possibilities of particle-based discrete element method (DEM) and cellular automaton methods. Emergent advantages of the developed approach to formulation of many body interaction are discussed. Main of them are its applicability to various realizations of the concept of discrete elements and a possibility to realize various rheological models (including elastic-plastic or visco-elasticplastic) and models of fracture to study deformation and fracture of solid-phase materials and media. Capabilities of particle-based modeling of heterogeneous solids are demonstrated by the problem of simulation of deformation and fracture of particle-reinforced metal-ceramic composites. 
Highlights
A modern theoretical approach used for description of heterogeneous solid is based on one of two concepts of representations of the medium: continuum or discrete
The group of particle-based numerical methods belonging to the concept of discrete elements (DE) is an extensively used and efficient tool to study complex processes of deformation and fracture of heterogeneous solids under complex loading conditions
The main advantage of these methods compared to conventional numerical methods in continuum mechanics (FEM, FDM and other) is a capability of direct modeling of numerous fracture accompanied by sliding and repacking of fragments, dilatancy of the medium and so on
Summary
A modern theoretical approach used for description of heterogeneous solid is based on one of two concepts of representations of the medium: continuum or discrete. Their mean value is used in the proposed model
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