Unusual extension–torsion–inflation couplings in pressurized thin circular tubes with helical anisotropy
Raushan Singh, Pranjal Singh and Ajeet Kumar
We present a thin tube formulation for coupled extension–torsion–inflation deformation in helically reinforced pressurized circular tubes. Both compressible and incompressible tubes are considered. On applying the thin tube limit, the nonlinear ordinary differential equation to obtain the in-plane radial displacement is converted into a set of two simple algebraic equations for the compressible case and one equation for the incompressible case. This allows us to obtain analytical expressions, in terms of the tube’s intrinsic twist, material constants, and the applied pressure, which can predict whether such tubes would overwind/unwind on being infinitesimally stretched or exhibit positive/negative Poisson’s effect. We further show numerically that such tubes can be tuned to generate initial overwinding followed by rapid unwinding as observed during finite stretching of a torsionally relaxed DNA. Finally, we demonstrate that such tubes can also exhibit usual deflation initially followed by unusual inflation as the tube is finitely stretched.
Journal article
Singh, R., Singh, P., & Kumar, A. (2019). Unusual extension–torsion–inflation couplings in pressurized thin circular tubes with helical anisotropy. Mathematics and Mechanics of Solids, 24(9), 2694-2712.
PhD Thesis
Singh, R. (2019). Unusual coupled deformation and supercoiling in elastic rods with application to biomolecules (Doctoral dissertation-5859, IIT, Delhi).
Effect of Intrinsic Twist and Orthotropy on Extension–Twist–Inflation Coupling in Compressible Circular Tubes
Raushan Singh, Siddhant Kumar and Ajeet Kumar
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.
Journal article
Singh, R., Kumar, S., & Kumar, A. (2017). Effect of intrinsic twist and orthotropy on extension–twist–inflation coupling in compressible circular tubes. Journal of Elasticity, 128(2), 175-201.
PhD Thesis
Singh, R. (2019). Unusual coupled deformation and supercoiling in elastic rods with application to biomolecules (Doctoral dissertation-5859, IIT, Delhi).
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