Nearest neighbor distances in uniaxial fiber composites

Nearest neighbor distances (first and higher order) are an important class of spatial descriptors useful in Materials Science and other disciplines. This descriptor plays a very important role in the mechanical response and failure behavior of uniaxial composites. In the present article nearest neighbor distances for random mono-sized fibers in uniaxial fiber composites are studied using computer simulations. A simple expression (given below) is proposed for the mean values of first, second, and third order nearest neighbor distances.〈Hn〉〈Pn〉=1+Bnff0mnwhere, 〈Hn〉 is the mean nth nearest neighbor distance, f is volume fraction, 〈Pn〉 is corresponding mean nearest neighbor distance for a point process and f0 is a constant. The quantities Bn and mn are constants for a given n. The predictions of this equation are in good agreement with the simulated results. This expression is applicable over the complete volume fraction range of 0 to π/12.