The theory of generalized thermoelasticity with fractional order strain for dipolar materials with double porosity

Chirilă, Adina; Marín, Marín

doi:10.1007/s10853-017-1785-z

Cited by 22 publications

(6 citation statements)

References 22 publications

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“…Passarella and Tibullo consider in [29] the problem of backward in time for the thermo-microstretch elastic bodies. Similar results can be found in [30,31].…”

Section: Introductionsupporting

confidence: 89%

A Study of Deformations in a Thermoelastic Dipolar Body with Voids

et al. 2020

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In this paper, we consider the mixed initial boundary value problem in the context of a thermoelastic porous body having a dipolar structure. We intend to analyze the rate of decay of solutions to this problem to ensure that in a finite time, they become null. In our main result, we find that the combined contribution of the dipolar constitution of the body together with voids dissipation and thermal behavior cannot cause vanishing of the deformations in a finite time.

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“…Passarella and Tibullo consider in [29] the problem of backward in time for the thermo-microstretch elastic bodies. Similar results can be found in [30,31].…”

Section: Introductionsupporting

confidence: 89%

A Study of Deformations in a Thermoelastic Dipolar Body with Voids

et al. 2020

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“…Substitution of Equation into Equation yields

σ_{xx} = λ e + 2 μ \frac{\partial u}{\partial x} - α P - β T,

σ_{yy} = λ e - α P - β T,

σ_{zz} = λ e + 2 μ \frac{\partial w}{\partial z} - α P - β T,

σ_{xz} = μ ((), \frac{\partial u}{\partial z} + \frac{\partial w}{\partial x}) .

…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…A volumetric expansion can result in significant pressurization of the pore fluid depending on the degree of containment and the thermal and hydraulic properties of the fluid as well as the solid. There are limited numbers of papers that present an analytical solution for the poro‐thermo‐elasticity problems …”

Section: Introductionmentioning

confidence: 99%

“…There are limited numbers of papers that present an analytical solution for the porothermo-elasticity problems. [1][2][3][4][5][6][7][8] Problems of the interaction between the magnetic field and stress and strain in a thermoelastic solid are very important because it has many applications in the fields of geophysics and earth system sciences. The theory of magnetothermoelasticity is concerned with the effect of magnetic field on the elastic and thermoelastic deformations of solid materials.…”

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confidence: 99%

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On a magneto‐poro‐thermoelastic medium under the influence of the Seebeck effect

Abd‐Elaziz

Othman

2019

Num Anal Meth Geomechanics

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Summary In this study, the poro‐thermoelastic problem with the effect of the magnetic field and Seebeck parameter was investigated. Modified Ohm's law that includes effects of the temperature gradient (Seebeck effect) and charge density, as well as generalized Fourier's law with current density, is introduced. We applied normal mode analysis to solve the resulting nondimensional coupled equations and then investigated the effects that nondimensional displacements, temperature distribution, excess pore water pressure, stresses, and induced magnetic field exerted on the poro‐thermoelastic half‐space medium. Numerical analyses are given graphically on the square (2D) and cubic (3D) domains to illustrate the effects of the porosity parameter, magnetic field, and Seebeck parameter on the physical variables.

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“…There is an increasing interest in the process of bone remodeling, since several authors propose different approaches for describing this process, see [14], [15], [21], [26]. Moreover, there exist other models for describing bodies with porosity, see [9], [23]. A detailed account of different models for heat conduction is given in [13].…”

Section: Introductionmentioning

confidence: 99%