Fractional order theory of thermoelasticity
TLDR
In this paper, a new theory of thermoelasticity is derived using the methodology of fractional calculus, and a uniqueness theorem for this model is proved and a variational principle and a reciprocity theorem are derived.About:
This article is published in International Journal of Solids and Structures.The article was published on 2010-01-15 and is currently open access. It has received 445 citations till now. The article focuses on the topics: Fractional calculus & Variational principle.read more
Citations
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Journal ArticleDOI
On fractional thermoelasticity
TL;DR: In this article, two general models of fractional heat conduction for non-homogeneous anisotropic elastic solids are introduced and the constitutive equations for thermoelasticity theory are obtained.
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A novel generalized thermoelasticity model based on memory-dependent derivative
Ya-Jun Yu,Wei Hu,Xiaogeng Tian +2 more
TL;DR: In this article, a memory-dependent derivative (MDD) was introduced into the Lord and Shulman (LS) generalized thermoelasticity, which might be superior to fractional ones.
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Generalized thermo-viscoelasticity with memory-dependent derivatives
TL;DR: In this article, a generalized thermo-viscoelasticity theory with memory-dependent derivatives is constructed, and the governing coupled equations with time-delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to one-dimensional problem of a half-space.
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Effect of variable thermal conductivity on a half-space under the fractional order theory of thermoelasticity
TL;DR: In this article, the authors considered the problem of a half-space formed of a material with variable thermal conductivity and applied the theory of fractional order theory of thermoelasticity to the problem.
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Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer
Mitali Bachher,Nantu Sarkar +1 more
TL;DR: In this paper, a nonlocal theory of generalized thermoelastic materials with voids based on Eringen's nonlocal elasticity and Caputo fractional derivative is established.
References
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Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
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Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
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A generalized dynamical theory of thermoelasticity
TL;DR: In this article, a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of heat flow.
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Thermoelasticity and Irreversible Thermodynamics
TL;DR: In this article, a unified treatment of thermoelasticity by application and further developments of the methods of irreversible thermodynamics is presented, along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement.