Stability in constrained temperature-rate-dependent thermoelasticity

Amnah M. Alharbi, Nigel H. Scott

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Abstract

In an anisotropic temperature-rate-dependent thermoelastic material four plane harmonic waves may propagate in any direction, all dispersive and attenuated, and all stable in the sense that their amplitudes remain bounded in the direction of travel. In this paper, the material is additionally assumed to suffer an internal constraint of the deformation-temperature type, i.e. the temperature is a prescribed function of the deformation gradient. In this constrained thermoelastic material four waves continue to propagate but instabilities are now found. Constrained temperature-rate-dependent thermoelasticity is then combined with generalized thermoelasticity in which the rate of change of heat flux also appears in the heat conduction equation. Four waves again propagate but instabilities are found as before. Anisotropic and isotropic materials are both considered.
Original languageEnglish
Pages (from-to)1738-1763
Number of pages26
JournalMathematics and Mechanics of Solids
Volume22
Issue number8
Early online date24 Jan 2017
DOIs
Publication statusPublished - 1 Aug 2017

Keywords

  • Thermoelasticity
  • generalized thermoelasticity
  • deformation-temperature constraint
  • deformation-entropy constraint
  • second sound
  • stability

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