Beam stiffening when twisted

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?