Effect of Intrinsic Twist and Orthotropy on Extension–Twist–Inflation Coupling in Compressible Circular Tubes

Abstract

We present effects of intrinsic twist and material orthotropy on extension–twist–inflation coupling in circular tubes about their stress-free state. Simple analytical expressions for coupling stiffnesses corresponding to extension–twist, twist–inflation and extension–inflation couplings are obtained. We show that the sign of the extension–twist coupling stiffness, which governs initial overwinding/unwinding in tubes during their extension, is not just dependent on the tube’s intrinsic twist but also on two other parameters: ratio of the Young’s moduli in the lateral surface of orthotropic tube and the excess of the Poisson’s ratio from an isotropy condition. By tuning these two parameters, one can generate the counter-intuitive overwinding as reported earlier in the case of DNA. Similarly, we show that even with positive Poisson’s ratio, an intrinsically twisted tube could inflate on being stretched. We also present a scheme to obtain all the relevant stiffnesses of chiral single-walled carbon nanotubes from a “one-atom unit cell” calculation. These stiffnesses, when plotted vs. the nanotube’s chirality, exhibit interesting periodicity which has its origin in the 6-fold symmetry of graphene. This trend is captured in the continuum model for a nanotube when it is assumed to be comprised of three families of parallel fibers on its lateral surface.