Poisson Fibre Processes I: Fibre Phase

Abstract

So far, we have considered Poisson processes of points and of lines with no width and infinite length. Of course, real fibres have finite length and width, so they occupy space in the plane of the network and generate contacts only if their proximity and orientation relative to each other fulfil certain criteria. Over the next two chapters we will consider some statistics of random networks of fibres modelled as rectangles with finite length and width. We begin by considering thin networks that may be considered to exist in two dimensions only and proceed to develop models for materials with finite thickness that can be represented as multi-planar structures consisting of several layers of thin structures. In this chapter we concentrate on interactions between fibres and the distribution of mass in the plane of the network. We extend our analysis to consider the porous structure of random near-planar fibrous materials in Chapter 5.