Effects of fibre dispersion on the effective elastic properties of 2D overlapping random fibre composites

The present paper is dedicated to the numerical investigation of the effects of fibre dispersion on the effective elastic properties of 2D overlapping random fibre composites. The mechanical response of the composite material is related to the percolation phenomenon which occurs when the concentration of fibres is important. The main purpose of the present work is to investigate whether an inhomogeneous fibre dispersion can lead or not to a decrease in percolation threshold, and to a beneficial mechanical reinforcement. For that purpose, we consider a fast and relevant pixel-based FE simulation, the model with an n-order approximate geometry. Indeed, such a modelling turns out to be more convenient to easily set up large samples of RVEs, and estimates both the effective properties and the percolation threshold. The fibre distribution is generated according to a 2-scale Boolean scheme of circles which enables one to vary the state of dispersion. Numerical results are also provided which highlight the influence of the dispersion depending on different parameters of distribution such as the scale ratio, the density of fibres or the area fraction of circles. Other calculations extend the study to different morphological features of the fibre such as its orientation and its aspect ratio.