Temperature-Rate-Dependent Thermoelasticity Theory With Memory-Dependent Derivative: Energy, Uniqueness Theorems, and Variational Principle
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Abstract This article is focused on developing a new mathematical model on the temperature-rate-dependent thermoelasticity theory (Green–Lindsay), using the methodology of memory-dependent derivative (MDD). First, the energy theorem of this model associated with two relaxation times in the context of MDD is derived for homogeneous, isotropic thermoelastic medium. Second, a uniqueness theorem for this model is proved using the Laplace transform technique. A variational principle for this model is also established. Finally, the results for Green–Lindsay model without MDD and coupled theory are obtained from the considered model.
2016 ◽
Vol 23
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pp. 195-208
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2003 ◽
Vol 38
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pp. 53-64
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2020 ◽
Vol 13
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pp. 24-38
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2021 ◽
Vol 147
(3)
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pp. 04021003