On the fabric tensor of polydisperse granular materials in 2D

The trace of the fabric tensor in static, isotropic, two-dimensional, frictionless, polydisperse granular materials is examined theoretically and numerically. In the monodisperse case, the trace of the fabric tensor equals the product of volume fraction and coordination number-thus the fabrics trace can be seen as contact density. For various size distributions, we obtain a correction factor to the monodisperse observation, which involves the first three moments of the particle size distribution function. The theoretical prediction is found to be in good agreement with numerical simulations of static frictionless systems.