Uniform extension–torsion of helical birods

Abstract

An analytical formulation is presented to study uniform extension–torsion behavior of helical birods. The uniformity in extension and compression reduces the set of governing nonlinear differential equations of birod theory to a set of nonlinear algebraic equations for the relevant unknown variables of a birod. Upon normalizing the algebraic equations, we note that the birod’s coupled extension–torsion behavior in its natural state can be tuned by changing the birod’s constituent strand’s intrinsic curvature and twist, Poisson’s ratio and the birod’s stiffness parameters corresponding to inter-strand separation and rotation. Analytical expressions of the birod’s extensional stiffness, torsional stiffness, extension–torsion coupling stiffness, effective Poisson’s ratio, overwinding/unwinding effect etc. in the birod’s natural state are obtained. In particular, we show that depending on the parameters chosen, a torsionally relaxed birod can undergo non-intuitive slow overwinding followed by rapid unwinding during its stretching as observed during pulling of a torsionally relaxed DNA.