A direct FEM approach for particulate reinforced elastic solids

In this work we are interested to provide an alternative way to model particulate composites by the Finite Element Method. Our proposal allows the inclusion of particles with any geometry, quantity and any regular or random arrangement in continuous matrix. Accordingly, the main feature of the formulation is: maintaining the geometry and the discretization of the matrix, to introduce a given distribution of particles without increasing the number of degrees of freedom or change the initial mesh of the problem. In this sense a direct FEM approach for particulate composites arise.Here, both the matrix and particles are considered elastic and totally connected, i.e., degeneration of the involved materials is not allowed and perfect adherence between matrix and particles phases is adopted, thus the interface or the transition zone between phases is not modeled.The proposed formulation already includes geometrically exact description allowing the development of large displacements and moderate strains. Examples are presented to validate the formulation confronting it with usual techniques of homogenization and laboratory experiments. Furthermore, the possibilities of the proposed technique are shown in an original example.