Compressional Energy of the Random Fiber Assembly

In this paper, we describe the method used to evaluate the theory of the compressional energy of the random fiber assembly, which was developed mathematically in Part I. We also introduce a mathematical derivation of the method for updating the orientation density function of fibers in a general fiber assembly. In order to evaluate the energy, the distribution of the fiber segment lengths is characterized using the gamma distribution. In addition, the curvature of the fiber segments is characterized by an equation that relates the crimp and the effective diameter of the crimped fiber configuration. We use minimization technique to compute the compressional energy. Effects of the mechanical properties of fibers and the structural parameters of the assembly on the minimum compressional energy are computed for New Zealand wools. Except for fiber crimp, there is good agreement between the computed results and experimental results for the various fiber and structural parameters. The model shows that if only fiber crimp is increased for a given initial geometry, the tangent compression modulus actually decreases. However, this point cannot be tested because crimpier fibers cannot be brought to the same initial geometry without generating nonzero compressional strain energy. We plan further investigation of this point.