Variational principle and reciprocity theorem on the temperature-rate-dependent poro-thermoelasticity theory

2021 ◽  
Author(s):  
Om Namha Shivay ◽  
Santwana Mukhopadhyay
Keyword(s):  
Variational Principle ◽  
Reciprocity Theorem ◽  
Rate Dependent ◽  
Thermoelasticity Theory ◽  
Temperature Rate

Temperature-Rate-Dependent Thermoelasticity Theory With Memory-Dependent Derivative: Energy, Uniqueness Theorems, and Variational Principle

2020 ◽  
Vol 142 (10) ◽  
Author(s):  
Biswajit Singh ◽  
Indranil Sarkar ◽  
Smita Pal (Sarkar)
Keyword(s):  
Variational Principle ◽  
Relaxation Times ◽  
Thermoelastic Medium ◽  
Rate Dependent ◽  
Thermoelasticity Theory ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Temperature Rate ◽  
With Memory ◽  
Coupled Theory

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.

Hyperbolic Thermoelasticity: A Review of Recent Literature

1998 ◽  
Vol 51 (12) ◽  
pp. 705-729 ◽  
Author(s):  
D. S. Chandrasekharaiah
Keyword(s):  
Recent Literature ◽  
Thermal Relaxation ◽  
Phase Lag ◽  
Lag Effects ◽  
The Past ◽  
Rate Dependent ◽  
Thermoelasticity Theory ◽  
Characteristic Features ◽  
Temperature Rate ◽  
Without Energy Dissipation

This review article is a continuation of a previous article by the author, Thermoelasticity with second sound: A review, which appeared in this journal in March, 1986 (Appl Mech Rev39(3) 355-376). Here, attention is focused on papers published during the past 10-12 years. Contributions to the theory of thermoelasticity with thermal relaxation and the temperature-rate dependent thermoelasticity theory are reviewed. The recently developed theory of thermoelasticity without energy dissipation is described, and its characteristic features highlighted. A glance is made at the new thermoelasticity theory which includes the so-called dual-phase-lag effects. There are 338 references.

On the Temperature-Rate Dependent Two-Temperature Thermoelasticity Theory

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Om Namha Shivay ◽  
Santwana Mukhopadhyay
Keyword(s):  
Constitutive Relations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Present Theory ◽  
Temperature Relation ◽  
Space Problem ◽  
Rate Dependent ◽  
Thermoelasticity Theory ◽  
Temperature Rate ◽  
Two Temperature

Abstract This work aims to formulate the temperature-rate dependent two-temperature (TRDTT) theory of thermoelasticity. The two-temperature thermoelasticity theory and the temperature-rate dependent thermoelasticity theory are two well-established thermoelasticity theories, which are developed from the generalized thermodynamic principles independently. Although the constitutive equations for TRDTT theory have been introduced, the formulation for the theory from the thermodynamical principles is not yet derived. Therefore, this work is an attempt to establish the theory from the generalized laws of thermodynamics and derive all the governing equations and constitutive relations for the theory. We derive a new and more general two-temperature relation that involves the temperature-rate terms of conductive and thermodynamic temperatures. We observe that this relation is different from the two-temperature relation reported in the literature. Further, we prove the uniqueness of solution for a general mixed initial boundary value problem in the context of linear modified TRDTT thermoelasticity theory for anisotropic medium. To investigate the effect of the present modified TRDTT theory, we solve a one-dimensional half-space problem and highlight the significance of the present theory.

Three-dimensional constitutive model for shape-memory polymers considering temperature-rate dependent behavior

2021 ◽  
Vol 30 (3) ◽  
pp. 035030
Author(s):  
Jinsu Kim ◽  
Seung-Yeol Jeon ◽  
Seokbin Hong ◽  
Yongsan An ◽  
Haedong Park ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Shape Memory ◽  
Three Dimensional ◽  
Shape Memory Polymers ◽  
Rate Dependent ◽  
Dependent Behavior ◽  
Temperature Rate

scholarly journals Stability in constrained temperature-rate-dependent thermoelasticity

2017 ◽  
Vol 22 (8) ◽  
pp. 1738-1763
Author(s):  
Amnah M Alharbi ◽  
Nigel H Scott
Keyword(s):  
Heat Conduction Equation ◽  
Deformation Gradient ◽  
Generalized Thermoelasticity ◽  
Rate Of Change ◽  
Harmonic Waves ◽  
Rate Dependent ◽  
Thermoelastic Material ◽  
Anisotropic Temperature ◽  
Temperature Rate ◽  
Anisotropic And Isotropic Materials

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.

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