A mathematical model of particle–particle interaction for discrete element based modeling of deformation and fracture of heterogeneous elastic–plastic materials

•A general expression for many-body force of interaction between discrete elements is formulated.•The methodology of determining the parameters of forces of element–element interaction is described.•The way to implement models of plasticity and fracture within the formalism of DEM is proposed.•Numerical examples show an important role of local pressure in fracture of brittle materials.

An approach to implementation of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of discrete element method (DEM) is proposed. The approach is based on constructing many-body forces of element–element interaction within the formalism of simply deformable element approximation of generalized concept of DEM. Implementation of the approach is shown by the example of the movable cellular automaton method, which integrates the possibilities of DEM and cellular automaton methods. For correct modeling of inelastic deformation and failure of heterogeneous materials the dilatational non-associated model of plastic flow is implemented within the formalism of DEM. The examples are presented which illustrate correctness of the developed mathematical formalism and its usefulness in analysis of various problems in mechanics of discontinua.