Homogenization technique for heterogeneous composite materials using meshless methods

This work is based on existing multi-scale numerical transition techniques suitable for simulating heterogeneous materials and makes use of two meshless methods-the Radial Point Interpolation Method (RPIM) and the Natural Neighbour Radial Point Interpolation Method (NNRPIM)-and the Finite Element Method (FEM). Representative volume elements (RVEs) are modelled and discretized using the three numerical methods. Prescribed microscopic displacements are imposed on different RVEs whose boundaries are periodic and, from the obtained stress field, the average stresses are determined. Consequentially, the effective elastic properties of a heterogeneous material are obtained for different fibre volume fractions. In the end, the numerical solutions are compared with the solutions proposed in the literature and it is proved that the NNRPIM achieve more accurate solutions than the RPIM and the FEM.