Material homogenization technique for composites: A meshless formulation

Abstract

The analysis of the structural behaviour of heterogeneous materials is a topic of research in the engineering field. Some heterogeneous materials have a macro-scale behaviour that cannot be predicted without considering the complex processes that occur in lower dimensional scales. Therefore, multi-scale approaches are often proposed in the literature to better predict the homogeneous mechanical properties of these materials. This work uses a multi-scale numerical transition technique, suitable for simulating heterogeneous materials, and combines it with a meshless method – the Radial Point Interpolation Method (RPIM) [1]. Meshless methods only require an unstructured nodal distribution to discretize the problem domain. In the case of the RPIM, the numerical integration of the integro-differential equation from the Galerkin weak form is performed using a background integration mesh. The nodal connectivity is enforced by the overlap of influence-domains defined in each integration point. In this work, using a plane-strain formulation, representative volume elements (RVE) are modelled and periodic boundary conditions are imposed on them. A computational homogenization is implemented and effective elastic properties of a composite material are determined. In the end, the solutions obtained using the RPIM and also a lower-order Finite Element Method are compared with the ones provided in literature.