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The importance of nonlinearities in material constitutive relations has longbeen appreciated in the continuum mechanics of macroscopic rods. Although themoment (torque) response to bending is almost universally linear for smalldeflection angles, many rod systems exhibit a high-curvature softening. Thesignature behavior of these rod systems is a kinking transition in which thebending is localized. Recent DNA cyclization experiments by Cloutier and Widomhave offered evidence that the linear-elastic bending theory fails to describethe high-curvature mechanics of DNA. Motivated by this recent experimentalwork, we develop a simple and exact theory of the statistical mechanics oflinear-elastic polymer chains that can undergo a kinking transition. Wecharacterize the kinking behavior with a single parameter and show that theresulting theory reproduces both the low-curvature linear-elastic behaviorwhich is already well described by the Wormlike Chain model, as well as thehigh-curvature softening observed in recent cyclization experiments.Comment: Revised for PRE. 40 pages, 12 figure

Exact theory of kinkable elastic polymers