Force distributions and force chains in random stiff fiber networks

We study the elasticity of random stiff fiber networks. The elastic
response of the fibers is characterized by a central force
stretching stiffness as well as a bending stiffness that acts
transverse to the fiber contour. Previous studies have shown that
this model displays an anomalous elastic regime where the
stretching mode is fully frozen out and the elastic energy is
completely dominated by the bending mode. We demonstrate by
simulations and scaling arguments that, in contrast to the bending
dominated elastic energy, the equally important elastic forces are
to a large extent stretching dominated. By characterizing these
forces on microscopic, mesoscopic and macroscopic scales we find
two mechanisms of how forces are transmitted in the network. While
forces smaller than a threshold Fc are effectively balanced by a
homogeneous background medium, forces larger than Fc are found to
be heterogeneously distributed throughout the sample, giving rise
to highly localized force chains known from granular media.