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[References: 73 tit.]

This paper develops an approach to model the deformation and fracture of heterogeneous materials atdifferent scales (including multiscale modeling) within a discrete representation of the medium.Within this approach, molecular dynamics is used for the atomic-scale simulation. The simply deformabledistinct element method is applied for simulating at higher length scales. This approach is proposedto be implemented using a general way to derive relations for interaction forces between distinct elementsin a many-body approximation similar to that of the embedded atom method. This makes it possibleto overcome limitations of the distinct element method which are related to difficulties inimplementing complex rheological and fracture models of solids at different length scales. For an adequatedescription of the mechanical behavior features of materials at the micro- and mesoscales, twokinds of models that consider grain and phase boundaries within the discrete element framework areproposed. Examples are given to illustrate the application of the developed formalism to the study ofthe mechanical response (including fracture) of materials with multiscale internal structure. The examplesshow that the simply deformable distinct element method is a correct and efficient tool for analyzingcomplex problems in solid mechanics (including mechanics of discontinua) at different scales.