Statistical geometry of random fibrous networks, revisited: Waviness, dimensionality, and percolation

Waviness alters both geometric and mechanical properties of stochastic fibrous networks and significantly affects overall mechanical response, but few results are available in the literature on the subject. In this work, we explore the importance of the dimension of constituent fibers (1D vs 2D) in determination of percolation thresholds, and other fundamental statistical properties of fibers having geometric waviness, in adaptation of classical theories on random lattices to practical applications, including analysis of nanotube ropes and collagen bundles. Although the so-called curl ratio clearly affects the statistical properties, as evaluated by Kallmes and Corte a few decades ago, we have found some results in this classic work to be inaccurate for systems containing fibers of moderate waviness. Our main findings include the independence of the mean number of crossings with regard to waviness, as well as the nonlinear dependence of probability of intersection on waviness. Our investigation of percolation in wavy fiber networks reveals that the percolation threshold is significantly increased, with increasing curl ratio. In addition, several nontrivial results related to network properties of infinite straight lines are also described, some of which are believed to have wide applications in practice. (C) 2004 American Institute of Physics.