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We propose a nonlinear extension of the standard tube model for semidilutesolutions of freely-sliding semiflexible polymers. Non-affine filamentdeformations at the entanglement scale, the renormalisation of directinteractions by thermal fluctuations, and the geometry of large deformationsare systematically taken into account. The stiffening response predicted forathermal solutions of stiff rods is found to be thermally suppressed. Instead,we obtain a broad linear response regime, supporting the interpretation ofshear stiffening at finite frequencies in polymerised actin solutions asindicative of coupling to longitudinal modes. We observe a destabilizing effectof large strains (about 100%), suggesting shear banding as a plausibleexplanation for the widely observed catastrophic collapse of in-vitrobiopolymer solutions, usually attributed to network damage. In combination withfriction-type interactions, our analysis provides an analytically tractableframework to address the nonlinear viscoplasticity of biological tissue on amolecular basis.

A unit-cell approach to the nonlinear rheology of biopolymer solutions