It is well recognized that matter has a discrete nature, but this aspect is usually considered only at the nano and microscale, on the other hand at the meso and macroscale levels compact matter is represented with a continuous model. At the macroscopic scales can be usefully adopted a discrete model of solids, without losing accuracy in the description of the main mechanical involved phenomena; when a multiscale study of solids is necessary the discrete approach, tailored to the scale of observation of interest, allows complete and exhaustive descriptions of many phenomena. This PhD thesis presents a general computational particle method suitable for analyzing the dynamic behaviour of compact solids as well as granular matters. The particle interaction is modelled through proper force functionals related to the nature of the material being analyzed (solid, granular or their interaction); such an approach is also adopted for the boundary and for the particle-particle contacts, so a unified mechanical model can be simply adopted for the simulation of a very wide class of mechanical problems under static or dynamic conditions. In particular the failure of brittle solids under dynamic dynamic impact can be easily predicted, avoiding the necessity of complex remeshing operations, stress field enrichment or the introduction of discontinuous displacement field, as typically required by numerical continuous approaches such as the finite element method. Moreover the discrete approach allows to simply model mechanical problems involving large displacements, friction or frictionless interactions with elastic boundaries, fragmentation and clustering of the failed material as well as cohesion in particle-like matters.Some examples aimed at demonstrating the versatility of the developed approach are finally presented: in particular the problems involving the failure of continuous solid elements under impact loading, confined particle flows and solid-granular materials interaction are simulated through the proposed approach and the related results are critically discussed and, when available, compared with literature data.
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