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For a particular cylindrical beam that is bent and twisted, its bending stiffness is found to increase with twist. I have a limited knowledge of continuum mechanics. Can the theory explain this, without introducing an ad hoc bending stiffness? For example, can twist-bending coupling explain it? If yes, how?

This is motivated by this paper where a biological polymer in bacteria is found to stiffen when twisted (and the controlled mechanical failure of this element is amazingly used by the organism to better move and survive). Of course a complex polymer is not a continuum beam, but here I wonder if continuum theory can be used, forgetting the microscopic structural details.

Also, do you know other examples where this stiffening occurs?

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    $\begingroup$ "For a particular cylindrical beam that is bent and twisted, its bending stiffness is found to increase with twist." Are you basing this only on the linked report of the bacterial hook or also on other reports? In elastic continuum beam theory, torsional shear is uncoupled with bending stiffness. $\endgroup$ Nov 17 '20 at 18:07
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    $\begingroup$ @Chemomechanics yes, the bacterial hook is the "particular" beam I refer to, and it's the only one I know (I ask if more examples are known). My question could be rephrased as "torsion and bending are uncoupled, how can one extend the theory to couple them?" $\endgroup$
    – scrx2
    Nov 17 '20 at 19:19
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    $\begingroup$ One possibility is implied in Block et al.'s "Compliance of bacterial flagella measured with optical tweezers" (which is cited by Son et al.): Actual molecules exhibit steric hindrance during torsion that increases the cross-sectional area and therefore the area moment of inertia. This isn't considered in standard beam theory, in which torsional deformation is considered isochoric. $\endgroup$ Nov 18 '20 at 6:58
  • $\begingroup$ one extra question: would you say that a beam where this stiffening occurs is necessarily a non linear element? $\endgroup$
    – scrx2
    May 25 at 7:25
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    $\begingroup$ Agreed; the bending is approximately linear for any given twist. But the outcome from twist and bending is not order independent; bending followed by twist isn’t identical to twist followed by bending (i.e., this loading doesn’t commute). I think your colleagues are using “nonlinear” somewhat loosely. $\endgroup$ May 26 at 16:24

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