The Direction Distribution on Cross-Contact Points in Anisotropic Fiber Assemblies

The spatial distribution and the volume density of points of fiber contact in a fiber assembly are dependent on the direction distribution function p( θ, ϕ) of the fiber segments. The expansion of the direction distribution function separates the terms associated with a uniformly-oriented fiber assembly from one of a generalized anisotropy. It is further demon strated that uniform fiber assemblies—other parameters being identical—consist of geometries in which the numbers of cross-contact points per unit length and per unit volume are maximized.