Postbuckling of chiral elastic rings with intrinsic twist

Abstract

Postbuckling of inextensible rings made from chiral filaments with intrinsic twist is studied. We show that the critical amount of intrinsic twist at which chiral elastic rings buckle might be greater than that at which buckling would occur with no chirality, dependent on degree of chirality and twist-to-bend ratio. Moreover, increasing the twisting rigidity relative to the bending rigidity of the filament can raise the critical amount of intrinsic twist, regardless of the degree of chirality. Lastly, on the basis of weakly nonlinear analysis, we find that the bifurcation is supercritical in the sense that the postbuckling solution of chiral elastic rings is stable for sufficiently large degree of chirality, regardless of the twist-to-bend ratio. This result is contrary to the postbuckling of elastic rings with intrinsic twist but no chirality in which the bifurcation is supercritical only for sufficiently large twist-to-bend ratio.