Compressional Energy of the Random Fiber Assembly

The compressional mechanism of a random fiber assembly is analyzed by an energy method. An infinitesimal fiber segment, which is bounded by two neighboring contact points, is chosen as the unit bending element. The geometry of this element is characterized by its arc length, curvature, and orientation. The change in bending energy of each fiber segment due to the compression of the assembly is derived in terms of the compressional strain and the Poisson's ratio of the assembly. The summation of each energy contribution is done using a continuous joint probability density function of the length and orientation of the segments.