We present a two-dimensional discrete model of solids that allows us to follow the bahavior of the solid body and of the fragments well beyond the formation of simple cracks. The model, consisting of polygonal cells connected via beams, is an extension of discrete models used to study granular flows. This modeling is particularly suitedfor the simulation of fracture and fragmentation processes. After calculating the macroscopic elastic moduli from the cell and beam parameters, we present a detailed study of an uniaxial compression test of a rectangular block, and of the dynamic fragmentation processes of solids in various experimental situations. The model proved to be successful in reproducing the experimentally observed subtleties of fragmenting solids.
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