Effect of size polydispersity on micromechanical properties of static granular materials

We analytically investigate the influence of particle size polydispersity on the micromechanical properties of granular packings. In order to approximate the macroscopic quantities in terms of the microscale details, we develop a meanfield approach. It is shown that the trace of the fabric and stress tensors, and the elements of the stiffness tensor can be expressed in terms of dimensionless correction factors (which depend only on the moments of the size distribution), besides the average packing properties such as packing fraction, mean coordination number, and mean normal force. The results of numerical simulations confirm the validity of our analytical predictions, as long as the size distribution is not too wide.