Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer
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.
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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TL;DR: In this article , a nonlocal model without energy dissipations is presented to investigate the impacts of the nonlocal thermoelastic parameters in a nanoscale material by the eigenvalue approach.
Abstract: In this work, a novel nonlocal model without energy dissipations is presented to investigate the impacts of the nonlocal thermoelastic parameters in a nanoscale material by the eigenvalue approach. The basic equations are applied under the Green and Naghdi model without energy dissipations. To obtain this model, the theory of the non-local continuum suggested by Eringen is applied. The Laplace transformation technique is used for the basic formulations to obtain the analytical solutions of the thermal stress, the displacement, and the temperature during the nanoscale thermo-electric medium. The inverse of the Laplace transformation is used with the numerical technique to obtain the complete solutions of the studying fields in the time–space domains. The main physical fields are displayed graphically and theoretically discussed under the influence of nonlocal parameters.
5 citations
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TL;DR: In this paper , a nonlocal theory for thermoelastic materials with voids and microtemperatures based on Mindlin's strain gradient theory was derived, which is a coupling of a two second-order in time equations with higher gradients terms due to the strain gradient length scale parameter l and the elastic nonlocal parameter ϖ coupled with two parabolic equations.
4 citations
TL;DR: In this article , the authors used the nonlocal continuum theory of Eringen to obtain the wave propagation in unbounded thermoelastic materials, and the integral transforms of the Laplace transform methods used to generate an analytical solution for physical variables are utilized to produce the analytical solutions for the thermal stress, displacement, and temperature distribution.
Abstract: In the current article, the nonlocal thermoelastic theory is used to discuss the wave propagation in unbounded thermoelastic materials. Due to the inclusion of relaxation time in thermal conduction formulation and the equations of motion, this model was developed using Lord and Shulman’s generalized thermoelastic model. The theory of the nonlocal continuum proposed by Eringen is used to obtain this model. The integral transforms of the Laplace transform methods used to generate an analytical solution for physical variables are utilized to produce the analytical solutions for the thermal stress, displacement, and temperature distribution. The effects of nonlocal parameters and relaxation time on the wave propagation distributions of physical fields for material are visually shown and explored.
4 citations
01 Mar 2021
TL;DR: In this article, three kinds of insulation materials, that is, polyurethane (PUR), foam concrete (FC) and vacuum insulation panel (VIP), were chosen to analyze their thermal conductivity under different kinds of weatherability experiments.
Abstract: The weatherability of insulation materials directly affects its thermal insulation performance, so it is necessary to carry out the weatherability experiments for insulation materials. In this paper, three kinds of insulation materials, that is, polyurethane (PUR), foam concrete (FC) and vacuum insulation panel (VIP) are chosen to analyze their thermal conductivity under different kinds of weatherability experiments. For the different kinds of weatherability experiments, the experiments of damp-heat, freeze-thaw, high-low temperature and wet-dry are designed to analyze the thermal conductivity of the insulation materials and the microstructure of insulation materials. The experimental results show that thermal conductivity of FC has a downward trend under the damp-heat experiment, and the thermal conductivity of FC has increased in other experiments. The thermal conductivity of PUR increases in all weatherability experiments, but the thermal conductivity of VIP does not change in all weatherability experiments.
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01 Jan 1962
TL;DR: In this article, the linearized theory of elasticity was introduced and the elasticity of a one-dimensional motion of an elastic continuum was modeled as an unbound elastic continuum.
Abstract: Preface Introduction 1 One-dimensional motion of an elastic continuum 2 The linearized theory of elasticity 3 Elastodynamic theory 4 Elastic waves in an unbound medium 5 Plane harmonic waves in elastic half-spaces 6 Harmonic waves in waveguides 7 Forced motions of a half-space 8 Transient waves in layers and rods 9 Diffraction of waves by a slit 10 Thermal and viscoelastic effects, and effects of anisotrophy and non-linearity Author Index Subject Index
4,133 citations
"Nonlocal theory of thermoelastic ma..." refers methods in this paper
...Laplace transform [45] together with an eigenvalue approach [33,46] technique is employed to obtain the closed form solutions in the transform domain....
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TL;DR: In this article, a theory of non-local elasticity is presented via the vehicles of global balance laws and the second law of thermodynamics via the use of a localized Clausius-Duhem inequality and a variational statement of Gibbsian global thermodynamics.
2,201 citations
TL;DR: In this article, a continuum theory of non-local polar bodies is developed for nonlinear micromorphic elastic solids, and the balance laws and jump conditions are given.
1,788 citations
681 citations
"Nonlocal theory of thermoelastic ma..." refers background in this paper
...In the last few years, fractional calculus has been successfully applied to extend generalized thermoelasticity theories to fractional order generalized thermoelasticity by Bachher et al. [33,34], Povstenko [35,36], Sherief [37], Youssef [38], Ezzat and his co-workers [39–43] etc. Rossikhin and Shitikova [44] applied fractional calculus to various problems of mechanics of solids....
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...Rossikhin and Shitikova [44] applied fractional calculus to various problems of mechanics of solids....
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TL;DR: A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed in this article.
Abstract: A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed. Because the heat conduction equation in the case 1≤α≤2 interpolates the parabolic equation (α = 1) and the wave equation (α = 2), the proposed theory interpolates a classical thermoelasticity and a thermoelasticity without energy dissipation introduced by Green and Naghdi. The Caputo fractional derivative is used. The stresses corresponding to the fundamental solutions of a Cauchy problem for the fractional heat conduction equation are found in one-dimensional and two-dimensional cases.
482 citations
"Nonlocal theory of thermoelastic ma..." refers background in this paper
...In the last few years, fractional calculus has been successfully applied to extend generalized thermoelasticity theories to fractional order generalized thermoelasticity by Bachher et al. [33,34], Povstenko [35,36], Sherief [37], Youssef [38], Ezzat and his co-workers [39–43] etc. Rossikhin and Shitikova [44] applied fractional calculus to various problems of mechanics of solids....
[...]
...[33,34], Povstenko [35,36], Sherief [37], Youssef [38], Ezzat and his co-workers [39–43] etc....
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