Thermoelasticity

Abstract

In this paper we consider an alternative generalization of classical thermoelasticity to those already available. Restrictions on constitutive equations are discussed with the help of an entropy production inequality proposed by Green and Laws [4]. The work is closely related to that of Miiller [3] but the final results are somewhat more explicit. The theory is linearized and a uniqueness theorem is stated. In agreement with Mfiller [3 ] it is shown that the linear heat conduction tensor is symmetric and that the theory allows for "second sound" effects. ABSTRAKTIn diesem Schreiben fiberlegen wit eine alternative Verallgemeinerung klassischer Thermo-Elastizit~it mit denjenigen schon vorhanden. Vorgeschlagen von Green und Laws [4]. Einschr~inkungen der konstitutiven Gleichungen sind diskutiert mit hilfe einer Entropie Produktions-Ungleichung. Die Arbeit ist eng im Zusammenhang mit derjenigen Miiller's [3] jedoch das Ergebniss ist deutlicher. Die Theorie ist linearisiert und ein einzigartiges Theorem festgestellt. Es wird gezeigt, in Ubereinstimmung mit MMler, [3] dass der lineare W~irmeleitung Tensor symmetrisch ist und dass die Theorie "second-sound" Wirkungen berticksichtigt.

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“…In contrast to the conventional coupled thermoelasticity theory (CTE) based on a parabolic heat equation [1], which predicts an infinite speed for the propagation of heat, these theories involve a hyperbolic heat equation and are referred to as generalized thermoelasticity theories. Among these generalized theories, the extended thermoelasticity theory (ETE) proposed by Lord and Shulman [2] and the temperature-rate dependent thermoelasticity theory (TRDTE) developed by Green and Lindsay [3] have been subjected to a large number of investigations. In view of the experimental evidence available in favour of finiteness of heat propagation speed, generalized thermoelasticity theories are considered to be more realistic than the conventional thermoelasticity theory in dealing with practical problems involving very large heat fluxes at short intervals, like those occurring in laser units and energy channels.…”

Fractional heat conduction equation for an infinitely generalized, thermoelastic, long solid cylinder

“…Green and Lindsay [3] developed the theory of thermoelasticity with two relaxation times which is based on a generalized inequality of thermodynamics. This theory does not violate Fourier's law of heat conduction when the body under consideration has a center of symmetry.…”

Effect of rotation on plane waves in generalized thermo-microstretch elastic solid with a relaxation time

“…The coupled theory of thermoelasticity has been extended by including the thermal relaxation time in the constitutive equations by Lord and Shulman [25] and Green and Lindsay [26]. These theories eliminate the paradox of infinite velocity of heat propagation and are termed generalized theories of thermo-elasticity.…”