An efficient stochastic and double-scale model to evaluate the effective elastic properties of 2D overlapping random fibre composites

This paper focuses on a stochastic and multi-scale finite element (FE) model to estimate the effective properties of 2D overlapping random fibre composites. We describe a new and efficient geometric approximation to solve different problems encountered when building the mesh in which the overlapping phenomenon between two or more fibres arises. The basic idea is to attain an approximation of the fibre geometry relative to quadrangular grid elements and an adaptive mesh refinement (AMR). Thus, the model allows one to obtain a fast, reliable and totally automated generation of a large number of representative volume elements (RVEs) of random fibre composites. Several numerical tests are performed to evaluate both the efficiency of the model and the reliability of the results. It can be noted that, here we only consider the mechanical response of the material in the framework of linear continuum mechanics.