  The problem of how staple yarns transmit tension is addressed within abstract
models in which the Amontons-Coulomb friction laws yield a linear programming
(LP) problem for the tensions in the fiber elements. We find there is a
percolation transition such that above the percolation threshold the
transmitted tension is in principle unbounded, We determine that the mean slack
in the LP constraints is a suitable order parameter to characterize this
supercritical state. We argue the mechanism is generic, and in practical terms
corresponds to a switch from a ductile to a brittle failure mode accompanied by
a significant increase in mechanical strength.
