Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer

doi:10.1080/17455030.2018.1457230

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Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer

Journal Article•DOI•

Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer

Mitali Bachher, Nantu Sarkar¹•Institutions (1)

University of Calcutta¹

02 Oct 2019-Waves in Random and Complex Media (Taylor & Francis)-Vol. 29, Iss: 4, pp 595-613

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.

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Abstract: A new nonlocal theory of generalized thermoelastic materials with voids based on Eringen’s nonlocal elasticity and Caputo fractional derivative is established. The one-dimensional form of the above...

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Journal Article•DOI•

Plane waves in nonlocal thermoelastic solid with voids

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Nantu Sarkar¹, Sushil K. Tomar²•Institutions (2)

University of Calcutta¹, Panjab University, Chandigarh²

22 Jan 2019-Journal of Thermal Stresses

TL;DR: In this paper, the propagation of time harmonic plane waves in an infinite nonlocal thermoelastic solid having void pores was studied, and the effects of frequency, void parameters, thermal parameter and nonlocality have been studied numerically on the phase speeds, attenuation coefficients and specific losses of all the propagating waves.

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Abstract: This work is concerned with the propagation of time harmonic plane waves in an infinite nonlocal thermoelastic solid having void pores. Three sets of coupled dilatational waves and an independent transverse wave may travel with distinct speeds in the medium. All these waves are found to be dispersive in nature, but the coupled dilatational waves are attenuating, while transverse wave is nonattenuating. Coupled dilatational waves are found to be influenced by the presence of voids, thermal field and elastic nonlocal parameter. While the transverse wave is found to be influenced by the nonlocal parameter, but independent of void and thermal parameters. For a particular model, the effects of frequency, void parameters, thermal parameter and nonlocality have been studied numerically on the phase speeds, attenuation coefficients and specific losses of all the propagating waves. All the computed results obtained have been depicted graphically and explained.

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68 citations

Cites background from "Nonlocal theory of thermoelastic ma..."

...Other symbols have their usual meanings and borrowed from [50]....
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...Field equations and constitutive relations Within the framework of Eringen’s theory of nonlocal elasticity [2], the constitutive relations for thermoelastic solid with voids are given by [50] 1 e2r2 ð Þtij 1⁄4 t ij 1⁄4 2leij x ð Þ þ kekk x ð Þ þ b/ x ð Þ ch x ð Þ 1⁄2 dij; (1) 1 e2r2 ð Þhi 1⁄4 hij 1⁄4 a/;i x ð Þ; (2) 1 e2r2 ð Þg 1⁄4 g 1⁄4 s _ / x ð Þ n/ x ð Þ bekk x ð Þ þmh x ð Þ; (3) 1 e2r2 ð Þqg 1⁄4 qg ð Þ 1⁄4 cekk x ð Þ þ ah x ð Þ þm/ x ð Þ; (4) where the quantities tL ij; h L i ; g L and ðqgÞ correspond the local thermoelastic solid with voids....
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Journal Article•DOI•

Waves in dual-phase-lag thermoelastic materials with voids based on Eringen’s nonlocal elasticity

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Sudip Mondal, Nihar Sarkar, Nantu Sarkar¹•Institutions (1)

University of Calcutta¹

09 Apr 2019-Journal of Thermal Stresses

TL;DR: The main idea of as mentioned in this paper is to extend Eringen's theory of nonlocal elasticity to generalized thermoelasticity with dual-phase-lag and voids.

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Abstract: The main idea of the present work is to extend Eringen’s theory of nonlocal elasticity to generalized thermoelasticity with dual-phase-lag and voids. Then we study the propagation of time harmonic ...

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65 citations

Cites background from "Nonlocal theory of thermoelastic ma..."

...This shows that x ¼ xc acts as a cutoff frequency for the existing transverse wave, a conclusion in accordance with that earlier mentioned by Sarkar and Tomar [14]....
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...(24), we see that the speed of transverse wave in thermoelastic medium with voids reduces to the classical transverse wave speed, a result recently obtained by Sarkar and Tomar [14] in the relevant medium when r 6¼ 1....
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...Within the framework of Eringen’s theory of nonlocal elasticity [1], the constitutive relations for thermoelastic solid with voids are given by [12,14] 1 e2r2 ð Þsij 1⁄4 sij 1⁄4 2leij þ kekk þ b/ ch ð Þdij; (1) 1 e2r2 ð Þhi 1⁄4 hij 1⁄4 a/;i; (2) 1 e2r2 ð Þg 1⁄4 g 1⁄4 s _ / n/ bekk þmh; (3) 1 e2r2 ð Þqg 1⁄4 qg ð Þ 1⁄4 cekk þ ahþm/; (4)...
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...Bachher and Sarkar [12] established a nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer....
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...Biswas and Sarkar [13] reported fundamental solution of the steady oscillations equations in porous thermoelastic medium with dual-phase-lag model....
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Journal Article•DOI•

A novel model of nonlocal thermoelasticity with time derivatives of higher order

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Ahmed E. Abouelregal¹•Institutions (1)

Mansoura University¹

30 Jul 2020-Mathematical Methods in The Applied Sciences

62 citations

Journal Article•DOI•

Transient response in a thermoelastic half-space solid due to a laser pulse under three theories with memory-dependent derivative

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Sudip Mondal, P. K. Pal¹, Mridula Kanoria¹•Institutions (1)

University of Calcutta¹

01 Jan 2019-Acta Mechanica

TL;DR: In this paper, a novel mathematical model of generalized thermoelasticity was proposed to investigate the transient phenomena due to the influence of a non-Gaussian pulsed laser type heat source in a stress free isothermal half-space in the context of Lord-Shulman (LS), dual-phase lag (DPL), and three phase lag (TPL) theories simultaneously.

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Abstract: Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of a non-Gaussian pulsed laser type heat source in a stress free isothermal half-space in the context of Lord–Shulman (LS), dual-phase lag (DPL), and three-phase lag (TPL) theories of thermoelasticity simultaneously. The memory-dependent derivative is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. Employing Laplace transform as a tool, the problem has been transformed to the space-domain, and it is then solved analytically. To get back all the thermophysical quantities as a function of real time, we use two Laplace inversion formulas, viz. Fourier series expansion technique (Honig in J Comput Appl Math10(1):113–132, 1984) and Zakian method (Electron Lett 6(21):677–679, 1970). According to the graphical representations corresponding to the numerical results, a comparison among LS, DPL, and TPL model has been studied in the presence and absence of a memory effect simultaneously. Moreover, the effects of a laser pulse have been studied in all the thermophysical quantities for different kernels (randomly chosen) and different delay times. Then, the results are depicted graphically. Finally, a comparison of results, deriving from the two numerical inversion formulas, has been made.

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49 citations

Journal Article•DOI•

Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on non-local Moore–Gibson–Thompson approach

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Ahmed E. Abouelregal¹, Hamid Mohammad-Sedighi², Ali Heidari Shirazi², Mohammad Malikan³, Victor A. Eremeyev³, Victor A. Eremeyev⁴ - Show less +2 more•Institutions (4)

Mansoura University¹, Shahid Chamran University of Ahvaz², Gdańsk University of Technology³, University of Cagliari⁴

29 Mar 2021-Continuum Mechanics and Thermodynamics

TL;DR: In this article, a computational analysis is conducted to study a magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium, where the medium is subjected to a periodic heat flow in the presence of a continuous longitude magnetic field.

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Abstract: In this investigation, a computational analysis is conducted to study a magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium. The medium is subjected to a periodic heat flow in the presence of a continuous longitude magnetic field. Based on Moore–Gibson–Thompson equation, a new generalized model has been investigated to address the considered problem. The introduced model can be formulated by combining the Green–Naghdi Type III and Lord–Shulman models. Eringen’s non-local theory has also been applied to demonstrate the effect of thermoelastic materials which depends on small scale. Some special cases as well as previous thermoelasticity models are deduced from the presented approach. In the domain of the Laplace transform, the system of equations is expressed and the problem is solved using state space method. The converted physical expressions are numerically reversed by Zakian’s computational algorithm. The analysis indicates the significant influence on field variables of non-local modulus and magnetic field with larger values. Moreover, with the established literature, the numerical results are satisfactorily examined.

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45 citations

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Journal Article•DOI•

Plane waves in nonlocal micropolar elasticity

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A. Cemal Eringen¹•Institutions (1)

Princeton University¹

01 Jan 1984-International Journal of Engineering Science

TL;DR: In this paper, the transverse plane wave dispersion in linear, non-local micropolar elastic solids is derived by equating the frequency of the Transverse Acoustical (TA) branch at the end of the Brillouin zone.

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278 citations

"Nonlocal theory of thermoelastic ma..." refers background or methods in this paper

...For the purpose of numerical computations, we have adopted the values of relevant material parameters from Eringen [18], Sing and Tomar [28], and Puri and Cowin [48]....
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...Eringen also studied plane waves in nonlocal micropolar elasticity [18]....
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...Eringen extended the concept of nonlocality to various other fields into his works cited in [7–10]....
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...Somenonclassical thermoelasticity theories have beendevelopeddepending on the strategies to incorporate additional atomistic features based on Eringen’s nonlocal elasticity theory [1] which is a widely celebrated one....
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...Eringen [16] investigated Rayleigh surface waves with small wavelengths under the nonlocal theory of elasticity....
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Journal Article•DOI•

Plane waves in linear elastic materials with voids

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Pratap Puri¹, Stephen C. Cowin²•Institutions (2)

University of New Orleans¹, Tulane University²

01 Jun 1985-Journal of Elasticity

TL;DR: In this article, the behavior of plane harmonic wave in a linear elastic material with voids is analyzed and two dilational waves in this theory, one is predominantly the dilational wave of classical linear elasticity and the other is predominantly a wave carrying a change in the void volume fraction.

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Abstract: The behavior of plane harmonic waves in a linear elastic material with voids is analyzed. There are two dilational waves in this theory, one is predominantly the dilational wave of classical linear elasticity and the other is predominantly a wave carrying a change in the void volume fraction. Both waves are found to attenuate in their direction of propagation, to be dispersive and dissipative. At large frequencies the predominantly elastic wave propagates with the classical elastic dilational wave speed, but at low frequencies it propagates at a speed less than the classical speed. It makes a smooth but relatively distinct transition between these wave speeds in a relatively narrow range of frequency, the same range of frequency in which the specific loss has a relatively sharp peak. Dispersion curves and graphs of specific loss are given for four particular, but hypothetical, materials, corresponding to four cases of the solution.

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256 citations

"Nonlocal theory of thermoelastic ma..." refers methods in this paper

...For the purpose of numerical computations, we have adopted the values of relevant material parameters from Eringen [18], Sing and Tomar [28], and Puri and Cowin [48]....
[...]

Journal Article•DOI•

Fractional catteneo-type equations and generalized thermoelasticity

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Yuriy Povstenko¹•Institutions (1)

Jan Długosz University¹

11 Jan 2011-Journal of Thermal Stresses

TL;DR: In this paper, the generalized Cattaneo-type equations with time-fractional derivatives are considered and the corresponding theory of thermal stresses is formulated, interpolating the theory of Lord and Shulman and thermoelasticity without energy dissipation of Green and Naghdi.

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Abstract: Following Compte and Metzler, the generalized Cattaneo-type equations with time-fractional derivatives are considered. The corresponding theory of thermal stresses is formulated. The proposed theory, on the one hand, interpolates the theory of Lord and Shulman and thermoelasticity without energy dissipation of Green and Naghdi and, on the other hand, generalizes theory of thermal stresses based on the fractional heat conduction equation. The fundamental solution to the nonhomogeneous fractional telegraph equation as well as the corresponding stresses are obtained in one-dimensional and axisymmetric cases.

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219 citations

Journal Article•DOI•

On the thermodynamics of systems with nonlocality

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Dominic G.B. Edelen¹, Dominic G.B. Edelen², Norman Laws¹, Norman Laws²•Institutions (2)

Cranfield University¹, Lehigh University²

01 Oct 1971-Archive for Rational Mechanics and Analysis

212 citations

"Nonlocal theory of thermoelastic ma..." refers background in this paper

...) have been proposed by Edelen and his co-authors [5,6]....
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Journal Article•DOI•

Nonlocal continuum mechanics

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Dominic G.B. Edelen¹, A. E. Green¹, Norman Laws¹•Institutions (1)

Lehigh University¹

01 Oct 1971-Archive for Rational Mechanics and Analysis

TL;DR: In this paper, the conservation laws of nonlocal continuum mechanics are derived from the conservation of energy and the invariance conditions under superposed rigid body motions, and the theory of non-local thermoelasticity is reconsidered in the light of recent developments in thermodynamics.

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Abstract: : It is shown in this paper that the conservation laws of nonlocal continuum mechanics are equivalent to, and can be derived from, the conservation of energy and the invariance conditions under superposed rigid body motions. Also, the theory of nonlocal thermoelasticity is reconsidered in the light of recent developments in thermodynamics, taking invariance conditions fully into account. (Author)

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182 citations