Mechanical and thermal couplings in helical strands*

Dansong Zhang, Martin Ostoja-Starzewski, Loïc Le Marrec

Research output: Contribution to journalArticlepeer-review


A generalized Timoshenko rod model is developed for helical strands and helically reinforced cylinders. The thermomechanical constitutive law has five effective elastic moduli, and two thermal coefficients, which can be obtained with the finite element method, or partly from analytic solutions. The model predicts nonclassical bending and thermoelastic behavior of helical strands. First, bending–shearing coupling is explicitly captured, which leads to non-planar bending under a transverse shear force, or a bending moment. Second, torsion and thermal expansion are coupled due to structural chirality. The dispersion relation of harmonic thermoelastic waves is governed by four non-dimensional parameters: two thermoelastic coupling constants, one chirality parameter and the Fourier number. The quasi-longitudinal and the quasi-torsional waves (“quasi” meaning the longitudinal mode is always coupled with a small torsional motion, and vice versa, due to chirality) are dispersive and damped, and dependent on temperature. The adiabatic-isothermal transition of the wave propagation is determined by the Fourier number.

Original languageEnglish (US)
Pages (from-to)185-212
Number of pages28
JournalJournal of Thermal Stresses
Issue number1
StatePublished - Jan 2 2019


  • Helix
  • Timoshenko rod model
  • adiabatic-isothermal transition
  • bending-shearing coupling
  • chirality
  • helical strand
  • thermoelastic coupling

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics


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