A modified Green–Lindsay thermoelasticity with strain rate to eliminate the discontinuity

Yu, Ya Jun; Xue, Zhangna; Tian, Xiaogeng

doi:10.1007/s11012-018-0843-1

Cited by 65 publications

(21 citation statements)

References 35 publications

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“…θ 0 is the uniform absolute temperature in the reference configuration, b i and r are the supply terms, (u i ) is the displacement vector, θ is the relative temperature and τ 0 , τ 1 are two parameters that satisfy (see [10], eq. 22)…”

Section: Equations and Assumptionsmentioning

confidence: 99%

“…The meaning of the assumptions in (i) is clear. Condition (ii) can be understand in terms of the elastic stability and condition (iii) is related with the well-known property of a heat conductor (see also [10], eq. 19).…”

Section: Equations and Assumptionsmentioning

confidence: 99%

“…This last one is based in a generalized dissipation inequality by considering a scalar function depending upon the temperature and its rate. In this short note we are going to be involved with a recent modification of this theory proposed in [10]. In that paper the authors introduce a second order tensor depending on the strain and its rate and a generalized Clausius-Duhem inequality.…”

Section: Introductionmentioning

confidence: 99%

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

Quintanilla

2018

Meccanica

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In this short note we consider a recent modification of the Green-Lindsay thermoelastic theory proposed at [10]. We consider a functional defined on the solutions of the problem. It allows us to obtain the continuous dependence of the solutions with respect to the initial conditions and to the supply terms, the time exponential decay of solutions and an alternative of Phragmén-Lindelöf type for the spatial behaviour.

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Section: Equations and Assumptionsmentioning

confidence: 99%

Section: Equations and Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Quintanilla

2018

Meccanica

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“…Following the notable work of Green and Lindsay [4], recently, Yu et al. [23] established a new model of generalized thermoelasticity theoretically by considering the strain rate term in the Green–Lindsay (GL) model [4] of generalized thermoelasticity with the aid of extended thermodynamics. A problem of semi‐infinite one‐dimensional thermoelastic medium with traction free at one end and subjected to a temperature rise using the Laplace transform method is also studied by Yu et al.…”

Section: Introductionmentioning

confidence: 99%

“…A problem of semi‐infinite one‐dimensional thermoelastic medium with traction free at one end and subjected to a temperature rise using the Laplace transform method is also studied by Yu et al. [23]. They observed that the strain rate may eliminate the discontinuity of the displacement at the elastic and thermal wavefronts.…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic plane waves under the modified Green–Lindsay model with two‐temperature formulation

Sarkar

Mondal²

2020

Z Angew Math Mech

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The present study is concerned with the reflection and propagation of thermoelastic plane waves from the stress‐free and thermally insulated surface of a homogeneous, isotropic thermally conducting elastic half‐space in the frame of modified Green–Lindsay theory of generalized thermoelasticity with two‐temperature (2TMGL). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exists one independent vertically shear‐type (SV‐type) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV‐type wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the amplitude ratios and their respective energy ratios for reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on the free surface. The paper concludes with the numerical results on the phase speeds, amplitude ratios and their respective energy ratios for specific parameter choices. Various graphs have been plotted to analyze the behavior of these quantities. The characteristics of employing the 2TMGL model are discussed by comparing the numerical results obtained for the present model with those obtained in case of the two‐temperature Green–Lindsay (2TGL) and two‐temperature Lord–Shulman (2TLS) models.

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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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A modified Green–Lindsay thermoelasticity with strain rate to eliminate the discontinuity

Cited by 65 publications

References 35 publications

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

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

Thermoelastic plane waves under the modified Green–Lindsay model with two‐temperature formulation

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

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