FAILURE OF PLANAR FIBER NETWORKS

We study the failure of planar random fiber networks with computer sim ulations. The networks are grown by adding flexible fibers one by one on a growing deposit [K. J. Niskanen and M. J. Alava, Phys. Rev. Lett. 73, 3475 (1994)], a process yielding realistic three dimensional netw ork structures. The network thus obtained is mapped to an electrical a nalogue of the elastic problem, namely to a random fuse network with s eparate bond elements for the fiber-to-fiber contacts. The conductivit y of the contacts (corresponding to the efficiency of stress transfer between fibers) is adjustable. We construct a simple effective medium theory for the current distribution and conductivity of the networks a s a function of intra-fiber current transfer efficiency. This analysis compares favorably with the computed conductivity and with the fractu re properties of fiber networks with varying fiber flexibility and net work thickness. The failure characteristics are shown to obey scaling behavior, as expected of a disordered brittle material, which is expla ined by the high current end of the current distribution saturating in thick enough networks. For bond breaking, fracture load and strain ca n be estimated with the effective medium theory. For fiber breaking, w e find the counter-intuitive result that failure is more likely to nuc leate far from surfaces, as the stress is transmitted more effectively to the fibers in the interior. (C) 1997 American Institute of Physics .