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A general approach to realization of models of elasticity, plasticity and fracture of heterogeneousmaterials within the framework of particle-based numerical methods is proposed in the paper. It is based onbuilding many-body forces of particle interaction, which provide response of particle ensemble correctlyconforming to the response (including elastic-plastic behavior and fracture) of simulated solids. Implementationof proposed approach within particle-based methods is demonstrated by the example of the movable cellularautomaton (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 manybodyinteraction are discussed. Main of them are its applicability to various realizations of the concept ofdiscrete 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 simulationof deformation and fracture of particle-reinforced metal-ceramic composites

Development of a formalism of movable cellular automaton method for numerical modeling of fracture of heterogeneous elastic-plastic materials