Mechanics of three-dimensional, nonbonded random fiber networks

The mechanical behavior of an ensemble of athermal fibers forming a nonbonded network subjected to triaxial compression is studied using a numerical model. The response exhibits a power law dependence of stress on the dilatation strain and hysteresis upon loading and unloading. A stable hysteresis loop results after the first loading and unloading cycle. In the early stages of compaction, strain energy is associated primarily with the bending of fibers, while at higher densities, it is stored primarily in the axial deformation mode. It is shown that the exponent of the power law, and the partition of energy in the axial and bending modes depends on the ratio of the bending to axial stiffness of the fibers. Accounting for interfiber friction does not change the functional form of the stress-strain relationship or the exponent. The central feature that distinguishes the mechanics of this system from that of bonded random networks is the relative sliding at contacts and the ensuing fiber rearrangements. We show that suppressing sliding leads to a much stiffer response. The results indicate that the value of the exponent of the stress-strain power law is determined not only by fiber bending and the formation of new contacts, but also by the relative sliding and axial deformation of fibers.