Homogenizing the Elastic Properties of Composite Material Using the NNRPIM

Abstract

The micro-heterogeneities existing in fiber composite materials usually restrain the use of macromechanical analysis. The complexity of the microstructure plays an important role in the overall material behavior and at times it cannot be discarded. Thus, multi-scale numerical transition techniques and homogenization procedures are used to compute effective elastic properties, creating a homogeneous medium mechanically equivalent to the original complex heterogeneous medium. This work proposes a new numerical tool, using a meshless method – the Natural Neighbor Radial Point Interpolation Method (NNRPIM) – to homogenize the elastic properties of fiber composite materials. Representative volume elements (RVEs) are used and discretized using the NNRPIM which only requires an unstructured nodal distribution to perform that discretization. The numerical integration of the discrete system of equations is computed using a nodal dependent integration mesh. In the NNRPIM, the nodal connectivity is enforced by the overlap of influence-cells constructed based on the Voronoï diagram. Prescribed macroscopic deformation gradients are imposed on different RVEs assuming periodic boundary conditions. From the obtained strain and stress fields, the effective elastic properties of a heterogeneous material are calculated. The meshless results are, in the end, compared with the FEM and literature solutions, proving the accuracy of the proposed approach.