  Cross-linked polymer networks with orientational order constitute a wide
class of soft materials and are relevant to biological systems (e.g., F-actin
bundles). We analytically study the nonlinear force-extension relation of an
array of parallel-aligned, strongly stretched semiflexible polymers with random
cross-links. In the strong stretching limit, the effect of the cross-links is
purely entropic, independent of the bending rigidity of the chains. Cross-links
enhance the differential stretching stiffness of the bundle. For hard
cross-links, the cross-link contribution to the force-extension relation scales
inversely proportional to the force. Its dependence on the cross-link density,
close to the gelation transition, is the same as that of the shear modulus. The
qualitative behavior is captured by a toy model of two chains with a single
cross-link in the middle.
