Numerical Evaluation of the Effective Elastic Properties of 2D Overlapping Random Fibre Composites

Abstract

We present a numerical investigation of the elastic coefficients of random fibre composites with high contrast of properties. Here we consider a numerical study based on the generation of representative volume elements (RVEs) with overlapping random fibre network. Such a concept requires an important Monte-Carlo draw of patterns as well as an accurate determination of RVE size. In this paper, this latter is done by estimating the evolution of the standard deviation according to the number of realizations for given values of RVE size. We consider the use of an appropriate model for an automatic, reliable and fast generation of RVEs : the model with an n-order approximate geometry that allows the construction of complex overlapping fibre network. It is well-established that the morphology of the microstructure greatly affects the mechanical response of such kind material. Some morphological features, namely orientation, aspect ratio and dispersion are investigated by considering them as random variables in the design of RVEs. The results are subsequently linked to the percolation phenomenon that occurs when fibres overlap and form some pathways inside the soft phase. This phenomenon influences effective properties of heterogeneous media, particularly in the case of a high contrast of properties.