On a Theory of Thermoelastic Materials with a Double Porosity Structure

Ieşan, D.; Quintanilla, R.

doi:10.1080/01495739.2014.914776

Cited by 109 publications

(81 citation statements)

References 26 publications

(37 reference statements)

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“…For Case 2, the thermal attenuation peak moved to the seismic band and the thermal wave is more wave‐like at these frequencies. Kumar et al (), based on the theory of Iesan and Quintanilla (), predict negative quality factors of the P wave, in this case, at the whole frequency range, despite the fact that the latter authors have shown the uniqueness of solutions as well as their stability when the internal energy is positive definite. Our attenuation factor is positive over all frequencies.…”

Section: Physics and Simulationsmentioning

confidence: 91%

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Physics and Simulation of Wave Propagation in Linear Thermoporoelastic Media

et al. 2019

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We develop a numerical algorithm for simulation of wave propagation in linear nonisothermal poroelastic media, based on Biot theory and a generalized Fourier law of heat transport in analogy with Maxwell model of viscoelasticity. A plane wave analysis indicates the presence of the classical P and S waves and two slow waves, namely, the Biot and the thermal slow modes of propagation, which present diffusive behavior under certain conditions, depending on viscosity, frequency, and the thermoelastic constants. The wavefield is computed with a direct meshing method using the Fourier differential operator to calculate the spatial derivatives. We propose two alternative time‐stepping algorithms, namely, a first‐order explicit Crank‐Nicolson method and a second‐order splitting method. The Fourier differential operator provides spectral accuracy in the calculation of the spatial derivatives. Modeling the thermal diffusive mode is relevant for high‐temperature high‐pressure fields and since it leads to mesoscopic attenuation by mode conversion of the fast waves to the thermal waves.

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Section: Physics and Simulationsmentioning

confidence: 91%

“…Iesan and Quintanilla () derive a theory of porothermoelasticity, based on a double porosity structure. This theory is not based on Biot equations and Darcy law, so that it is not directly comparable with ours.…”

Section: Introductionmentioning

confidence: 99%

Physics and Simulation of Wave Propagation in Linear Thermoporoelastic Media

et al. 2019

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“…Recently, on the basis of balance of equilibrated force the theories of elasticity and thermoelasticity for materials with a double porosity structure are presented by Ieşan and Quintanilla [19]. The basic threedimensional BVPs of the equilibrium theory of elasticity for materials with a double porosity structure are investigated by using the potential method (boundary integral equation method) and the theory of singular integral equations by Ieşan [18].…”

Section: Introductionmentioning

confidence: 99%

Fundamental solutions in the theory of elasticity for triple porosity materials

Svanadze

2015

Meccanica

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This paper concerns with the full coupled linear theory of elasticity for triple porosity materials. The system of the governing equations based on the equations of motion, conservation of fluid mass, the constitutive equations and Darcy's law for materials with triple porosity. The cross-coupled terms are included in the equations of conservation of mass for the fluids of the three levels of porosity and in the Darcy's law for materials with triple porosity. The system of general governing equations of motion is expressed in terms of the displacement vector field and the pressures in the three pore systems. Five spatial cases of the dynamical equations are considered: equations of steady vibrations, equations in Laplace transform space, equations of quasi-static, equations of equilibrium and equations of steady vibrations for rigid body with triple porosity. The fundamental solutions of the systems of these PDEs are constructed explicitly by means of elementary functions and finally, the basic properties of the fundamental solutions are established.

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“…Following Iesan and Quintanilla [42], the field equations and the constitutive relations for a homogeneous thermoelastic material with double porosity structure, when the Hall current is taken into account, can be written as: T T 0  , a superposed dot represents differentiation with respect to time variable t.…”

Section: Basic Equationsmentioning

confidence: 99%

Effect of Hall Current in Thermoelastic Materials with Double Porosity Structure

Kumar

Vohra²

2017

International Journal of Applied Mechanics and Engineering

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The present investigation is concerned with one dimensional problem in a homogeneous, isotropic thermoelastic medium with double porosity structure in the presence of Hall currents subjected to thermomechanical sources. A state space approach has been applied to investigate the problem. As an application of the approach, normal force and thermal source have been taken to illustrate the utility of the approach. The expressions for the components of normal stress, equilibrated stress and the temperature change are obtained in the frequency domain and computed numerically. A numerical simulation is prepared for these quantities. The effect of the Hartmann number is depicted graphically on the resulting quantities for a specific model. Some particular cases of interest are also deduced from the present investigation.

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On a Theory of Thermoelastic Materials with a Double Porosity Structure

Cited by 109 publications

References 26 publications

Physics and Simulation of Wave Propagation in Linear Thermoporoelastic Media

Physics and Simulation of Wave Propagation in Linear Thermoporoelastic Media

Fundamental solutions in the theory of elasticity for triple porosity materials

Effect of Hall Current in Thermoelastic Materials with Double Porosity Structure

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