Various types of fibers encountered in Network materials are presented and classified in this chapter. Their mechanical behavior is of primary concern here. The first section describes the structure and mechanical behavior of cellulose fibers, polymeric fibers used in nonwovens, and collagen fibers forming connective tissue. The remainder of the chapter is divided into three parts presenting the mechanical behavior of athermal fibers, thermal filaments, and of fiber bundles. The linear, nonlinear, and rupture characteristics of athermal fibers are presented. Thermal filaments, which form molecular networks such as elastomers and gels, are described by the Gaussian, Langevin, and self-avoiding random walk models. Models describing the mechanics of semiflexible filaments are presented. The section on the mechanics of fiber bundles presents a number of results relevant for bundles of continuous and discontinuous (staple) fibers, including the effect of bundle twisting and of packing on the axial stiffness and strength of the bundle. These results apply to many networks of practical importance which are composed from fiber bundles.

The previous three chapters cover the elastic behaviour of composites containing aligned fibres that are, in effect, infinitely long. Use of short fibres (or equiaxed particles) creates scope for using a wider range of reinforcements and more versatile processing and forming routes (see Chapter 15). There is thus interest in understanding the distribution of stresses and strains within such composites, and the consequences of this for the stiffness and other mechanical properties. In this chapter, brief outlines are given of two analytical models. In the shear lag treatment, a cylindrical (short fibre) reinforcement is assumed, with stress fields in fibre and matrix being simplified (leading to some straightforward analytical expressions). It introduces important concepts concerning load transfer mechanisms, although it is not very widely used for property prediction. The Eshelby method, on the other hand, is based on the reinforcement being ellipsoidal (anything from a sphere to a cylinder or a plate): the analysis is more rigorous, but with the penalty of greater mathematical complexity. The model is only briefly described here. Its use also introduces an important concept – that of a misfit strain, which is helpful in areas well beyond those of the mechanics of conventional composite materials.