Spatial Stability for the Quasi-Static Problem in Thermoelastic Diffusion Theory

Aouadi, Moncef

doi:10.1007/s10440-008-9299-y

Cited by 10 publications

(4 citation statements)

References 38 publications

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“…We assume that the region V from here on refers to a domain whose boundary V includes a plane portion S 0 (cf. [34]). The rectangular Cartesian coordinate frame is supposed to be chosen in such a way that the x 1 Ox 2 plane contains S 0 and V lies in the region x 3 > 0.…”

Section: A Decay Estimatementioning

confidence: 99%

Qualitative Results in the Theory of Thermoelastic Diffusion Mixtures

Aouadi

2010

Journal of Thermal Stresses

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The general equations of motion and constitutive equations are derived in a mixture of two interacting continua, taking into account the effects of heat and diffusion. First, the basic equations of the nonlinear theory of heat and diffusion conducting elastic mixtures are derived in lagrangian description. A frame independent nonlinear constitutive relation is derived. Then, the theory is linearized and field equations are given for both anisotropic and isotropic solids. The continuous dependence of solutions on initial data and body sources, and a uniqueness result are presented. An exponential decay estimate of the solutions is established. Finally, we prove the impossibility of the localization in time of the solutions.

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Section: A Decay Estimatementioning

confidence: 99%

Qualitative Results in the Theory of Thermoelastic Diffusion Mixtures

Aouadi

2010

Journal of Thermal Stresses

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“…One interesting question is, therefore, if the behavior of the solution with respect to the time variable remains unaltered in the quasi-static case. The number of contributions has increased over the last years (see, among others, [18][19][20][21]). In a recent article by Magaña and Quintanilla [22], they considered that this quasi-static hypothesis was also imposed in the volume fraction and in the temperature.…”

Section: Introductionmentioning

confidence: 99%

Quasistatic Porous-Thermoelastic Problems: An a Priori Error Analysis

2021

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In this paper, we deal with the numerical approximation of some porous-thermoelastic problems. Since the inertial effects are assumed to be negligible, the resulting motion equations are quasistatic. Then, by using the finite element method and the implicit Euler scheme, a fully discrete approximation is introduced. We prove a discrete stability property and a main error estimates result, from which we conclude the linear convergence under appropriate regularity conditions on the continuous solution. Finally, several numerical simulations are shown to demonstrate the accuracy of the approximation, the behavior of the solution and the decay of the discrete energy.

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“…Singh [17,18] studied the reflection phenomena of waves from the free surface of an elastic solid under theory of generalized thermodiffusion. Aouadi [19][20][21][22][23][24] reported some studies on thermoelastic diffusion and generalized thermoelastic diffusion. Subsequently, great attention has been paid to the theory of thermoelastic diffusion to investigate the nature of mutual interactions of mass diffusion with the temperature and strain fields, and it has been realized that the process of thermodiffusion could have a very considerable influence upon the deformation of the body (see Sharma [25], Sharma et al [26][27][28], Kumar and Kansal [29,30], Ram et al [31], Deswal and Choudhary [32][33][34], Elhagary [35] and Rong-hou et al [36]).…”

Section: Introductionmentioning

confidence: 99%

A study of influence of diffusion inside a spherical shell under thermoelastic diffusion with relaxation times

Kothari

Mukhopadhyay

2012

Mathematics and Mechanics of Solids

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The present work is concerned with the elasto-thermo-diffusion interactions inside a spherical shell whose inner and outer boundaries are traction free and are subjected to a step input in temperature under generalized thermoelastic diffusion. The chemical potential is also assumed to be a function of time on the boundaries of the shell. The problem is studied by employing three different theories of thermoelastic diffusion in a unified way. The integral transform technique is used to obtain the general solution. Using a numerical method and computer programming, the final solution in the physical domain is obtained. The results corresponding to thermoelastic medium, that is, in the absence of diffusion, are also found in a particular case. The influence of diffusion on variation of physical fields due to the cross effects arising from the coupling of temperature, diffusion and strain fields inside the shell is analyzed with the help of graphically plotted results of different field variables in the thermoelastic medium and thermoelastic diffusive medium. The variation of this influence with time under different theories is also discussed. The significant points are highlighted.

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Spatial Stability for the Quasi-Static Problem in Thermoelastic Diffusion Theory

Cited by 10 publications

References 38 publications

Qualitative Results in the Theory of Thermoelastic Diffusion Mixtures

Qualitative Results in the Theory of Thermoelastic Diffusion Mixtures

Quasistatic Porous-Thermoelastic Problems: An a Priori Error Analysis

A study of influence of diffusion inside a spherical shell under thermoelastic diffusion with relaxation times

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