A numerical investigation of the connection between state of dispersion and percolation and its effect on the elastic properties of 2D random microstructures

• The connection between state of dispersion and percolation is investi-gated.
• Mechanical improvements are expected for some heterogeneous media.
• Contrast e_ects are investigated as well.
• Possible mechanical reinforcements are highlighted when percolation is enhanced.
• Percolation e_ects are very sensitive to the contrast of properties.

The present work is dedicated to a numerical investigation of the connection between state of dispersion and percolation and its effect on the elastic properties of 2D random microstructures. The main objective consists in checking out the link between percolation and mechanical response in the context of a heterogeneous medium the reinforcements of which are not homogeneously dispersed. Besides, the influence of the stiffness of inclusions is also investigated since this could impact on the percolation effects. For these purposes, large samples of volume elements are generated according to the Monte Carlo method. We consider the low cost framework of 2D random grids which enables large and in-depth investigations. Besides, the spatial distribution of heterogeneities is simulated with the help of the 2-scale Boolean scheme of disks which is a powerful tool for modelling and studying several states of dispersion. The numerical results highlight beneficial mechanical reinforcements for a heterogeneous dispersion when the percolation phenomenon is enhanced. This improvement is highly sensitive to the stiffness of heterogeneities.