Some qualitative results for a modification of the Green–Lindsay thermoelasticity

Quintanilla, R.

doi:10.1007/s11012-018-0889-0

Cited by 22 publications

(4 citation statements)

References 18 publications

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“…For fully coupled thermal-stress problems this means that the influence of thermal shock affects the magnitude and pattern of temperature and stresses instantaneously in the solution process. The nonlinear equations of electro-magneto-porothermoelasticity applying MGL simulation and finite strain theory using Piola-Kirchhof stress is presented in this section [24][25][26][27]. The strain equation is considered based on the finite strain theory:…”

Section: The Generalized Thermoelasticity Equations Of Porous Mediums...mentioning

confidence: 99%

One-dimensional electro- magneto-poro-thermoelastic wave propagation in a functionally graded medium with energy dissipation

Mirparizi¹,

Zhang²,

Amiri³

2022

Phys. Scr.

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Laser-induced wave propagation and reflection phenomenon in a functionally graded porous medium subjected to electro- magnetic field is studied in the present research. Firstly, a modified generalized thermoelastic theory named Modified Green Lindsay (MGL) for wave propagation in a porous medium is developed. The properties of the medium are considered as a temperature-dependent nonlinear function. Furthermore, the influence of thermal and mechanical rates in the modified generalized equations are considered. An updated FEM and Newmark’s technique are applied to solve the time-dependent and nonlinear equations. The second Piola-Kirchhoff stress, temperature and displacement distributions in the body subjected to laser shock are presented graphically. Based on the results, the wave propagation amplitude in the body subjected to heat flux reduces over time because of the backplane influenced by convection heat transfer. Wave propagation is more obvious in MGL simulation outcomes compared to the classical ones. In addition, it is observed that the MGL simulation is superior in presenting more exact wave propagation in comparison to the simple GL theory. As the boundary condition receives the most energy due to the laser pulse, the maximum variations of the volume fraction are experienced in this boundary.

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Section: The Generalized Thermoelasticity Equations Of Porous Mediums...mentioning

confidence: 99%

One-dimensional electro- magneto-poro-thermoelastic wave propagation in a functionally graded medium with energy dissipation

Mirparizi¹,

Zhang²,

Amiri³

2022

Phys. Scr.

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“…[25] established a generalized thermoelastic model by using the strain rate in the G‐L theory of thermoelasticity and introduced the MG‐L theory of thermoelasticity. Quintanilla [26] discussed some qualitative results in the context of the MG‐L theory of thermoelasticity. In the frame of MG‐L theory of thermoelasticity with TT, Sarkar and Mondal [27] investigated the propagation of thermoelastic plane waves at a stress‐free and thermally insulated surface of a homogeneous, isotropic thermally conducting elastic half‐space.…”

Section: Introductionmentioning

confidence: 99%

Response of frequency domain in generalized thermoelastic medium under modified Green‐Lindsay with non‐local and two temperature

Kaushal,

Kumar,

Lofty

et al. 2024

Z Angew Math Mech

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This paper introduces a novel model for a generalized thermoelastic medium with homogeneity and isotropy, by applying the Modified Green‐Lindsay (MG‐L) theory of thermoelasticity. The focus is on analysing the deformation due to time‐harmonic by considering the impact of non‐local and two‐temperature (TT) parameters. The governing equations are solved using dimensionless quantities and a potential function. To address the boundary value problem in the frequency domain, the Hankel transform is employed. Specific boundary conditions, such as a normal force or thermal source, are applied. Analytical expressions for components of displacement, stresses, conductive temperature, and temperature distribution are derived in the transformed domain A numerical inversion technique is utilised to translate the solution into the physical domain. The study delves into exploring the influence of non‐local and two‐temperature parameters, as well as different theories of thermoelasticity on stresses, temperature distribution and conductive temperature. These effects are visually represented through graphical illustrations. Additionally, special cases of interest are examined and discussed.

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“…[12] (2018) proposed a modified Green‐Lindsay model by incorporating in Green‐Lindsay thermoelastic (G‐L) model with aid of extended thermodynamics. Quintanilla [13] proved the exponential decay of solutions and described the spatial behavior of these solutions for modified Green‐Lindsay thermoelasticity.…”

Section: Introductionmentioning

confidence: 99%

Response of impedance parameters on waves in the micropolar thermoelastic medium under modified Green‐Lindsay theory

2022

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The present study is focused on devoting a model to estimate the response of impedance parameters in micropolar with modified Green-Lindsay (MMGL) generalized thermoelastic medium. The problem of reflection phenomena is formulated and explained for the considered model. Amplitude ratios of various waves are obtained for the MMGL model, Green-Lindsay (G-L,1972) thermoelastic model, and Lord-Shulman (L-S,1967) thermoelastic model for longitudinal displacement wave (LD-wave), thermal wave (T-wave), coupled transverse (CD-I) wave and coupled micro-rotational (CD-II) wave. These amplitude ratios are the functions of the angle of incidence, frequency, and impedance parameters. The impact of impedance parameters on various reflection coefficients is displayed in the form of a graph. From the present study, certain cases are also deduced. 1Nomenclature: 𝜆, μ, Lame's constants; , γ 1 = (3𝜆 + 2𝜇 + K) 𝛼 t ,; 𝛼 t , the coefficient for linear thermal expansion,; K * , coefficient of thermal conductivity; t, time; t pq , components of stress; T, Temperature distribution; 𝜏 0 and 𝜏 1 , relaxation times; 𝛿 pq , Kronecker delta; 𝜌, C e , density, specific heat respectively; ⃗ u, displacement vector; 𝜂 1 , η 2 , η 3 and η 4 , constant; 𝜙 r , microrotation vector; 𝜉 pqr , alternating tensor; 𝛼, 𝛽, 𝛾, K, micropolar constants; T 0 , reference temperature; m pq , component of couple stress tensor; ∇ 2 , Laplacian operator.

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Some qualitative results for a modification of the Green–Lindsay thermoelasticity

Cited by 22 publications

References 18 publications

One-dimensional electro- magneto-poro-thermoelastic wave propagation in a functionally graded medium with energy dissipation

One-dimensional electro- magneto-poro-thermoelastic wave propagation in a functionally graded medium with energy dissipation

Response of frequency domain in generalized thermoelastic medium under modified Green‐Lindsay with non‐local and two temperature

Response of impedance parameters on waves in the micropolar thermoelastic medium under modified Green‐Lindsay theory

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