Thermomechanics of helical strands and helical-fiber-reinforced rods
type: CreativeWork
description: Helical strands, or helically wound cables, are made of layers of individual wires wrapped around a common central axis. They are seen in ropes and power transmission cables. Similar structures are also present in biological tissues in the form of helical fiber reinforced composites. Regardless of the distinct applications, the helical wrapping in all such structures introduces mirror asymmetry, i.e. chirality, resulting in effective properties not present in the base material. One most prominent effect of the presence of helices is the coupling between tension and torsion, which is widely modeled and studied in the literature. However, complex issues arise when there is bending. First, the effective bending stiffness is difficult to estimate and existing analytical models require careful validation. We conduct a full-fledged finite element analysis of the bending of a single layered helical strand, with internal friction and pretension. The effects of the pretension level, bending amplitude, and the friction coefficient on the effective bending stiffness are elucidated. Second, in the no-slip regime, the existing Euler-Bernoulli framework for helical strands is extended. A Timoshenko rod model is established for helical strands, with a 6 by 6 stiffness matrix governed by five independent elastic moduli. The model is capable of capturing the bending-shearing coupling in helical strands due to the underlying chirality, and correctly predicting the cross section forces and moments under several boundary value problems when compared with finite element results, whereas the existing Euler-Bernoulli model wrongly predicts particular forces or moments to be zero. The bending-shearing coupling is also demonstrated by the non-planar bending of helical strands under a single transverse force, or a single bending moment. The equations of vibration are then derived, with the eigenfrequencies and mode shapes identified. Due to chirality, the longitudinal and torsional modes are…
abstract: Helical strands, or helically wound cables, are made of layers of individual wires wrapped around a common central axis. They are seen in ropes and power transmission cables. Similar structures are also present in biological tissues in the form of helical fiber reinforced composites. Regardless of the distinct applications, the helical wrapping in all such structures introduces mirror asymmetry, i.e. chirality, resulting in effective properties not present in the base material. One most prominent effect of the presence of helices is the coupling between tension and torsion, which is widely modeled and studied in the literature. However, complex issues arise when there is bending. First, the effective bending stiffness is difficult to estimate and existing analytical models require careful validation. We conduct a full-fledged finite element analysis of the bending of a single layered helical strand, with internal friction and pretension. The effects of the pretension level, bending amplitude, and the friction coefficient on the effective bending stiffness are elucidated. Second, in the no-slip regime, the existing Euler-Bernoulli framework for helical strands is extended. A Timoshenko rod model is established for helical strands, with a 6 by 6 stiffness matrix governed by five independent elastic moduli. The model is capable of capturing the bending-shearing coupling in helical strands due to the underlying chirality, and correctly predicting the cross section forces and moments under several boundary value problems when compared with finite element results, whereas the existing Euler-Bernoulli model wrongly predicts particular forces or moments to be zero. The bending-shearing coupling is also demonstrated by the non-planar bending of helical strands under a single transverse force, or a single bending moment. The equations of vibration are then derived, with the eigenfrequencies and mode shapes identified. Due to chirality, the longitudinal and torsional modes are…
author: Zhang, Dansong
language: en
keywords: adiabatic-isothermal transition, telegraph equation, chirality, bending stiffness, stick-slip, contact, pretension, Timoshenko rod, finite element analysis, thermomechanical constitutive relation, vibration, eigenfrequency, bending-shearing coupling, thermal-torsional coupling, thermoelastic wave, discontinuity, phase velocity, group velocity, spectral finite element, Maxwell-Cattaneo heat conduction, dispersion relation, thermal relaxation time
date published: 2019-02-08T18:44:40Z
date modified: 2026-07-22T22:24:42Z
provider: University of Illinois - Urbana-Champaign
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Illinois at Urbana-Champaign

PropertyValue
property ID: Handle
value: http://hdl.handle.net/2142/102946