A Theory of Micropolar Thermoelasticity Without Energy Dissipation

Ciarletta, Michele

doi:10.1080/014957399280760

Cited by 69 publications

(38 citation statements)

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“…Chirita in [3] and Ciarletta in [4] studied the spatial behavior of the amplitude for a forced oscillation, in the case of a rhombic thermoelastic materials, provided the exciting frecquency is less than a certain critical frequency.…”

Section: Preliminary Resultsmentioning

confidence: 99%

“…If we take into consideration the constitutive equations (3) and the geometric equations (4), from the equations of motion (1) and equation of energy (2) we obtain a system of equations in terms of displacements u i , dipolar displacements ϕ ij and thermal variation τ , for any (x, t) ∈ B × (0, ∞), as…”

Section: Basic Equationsmentioning

confidence: 99%

“…A superposed dot denotes the differentiation with respect to time t, and a subscript preceded by a comma denotes the diferentiation with respect to the corresponding spatial variable. The basic system of equations of theory of anisotropic and homogeneous dipolar bodies in thermoelasticity without energy dissipation, consist of (see, for instance, [4]) -the equations of motion…”

Section: Basic Equationsmentioning

confidence: 99%

“…The theory without energy dissipation proposed in Ciarletta [4] allows propagation of thermal waves at a finite speed.…”

Section: Introductionmentioning

confidence: 99%

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Evolution of solutions for dipolar bodies in Thermoelasticity without energy dissipation

Marín

Abbas

2016

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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The aim of our paper is the study of the spatial evolution of vibrations in the context of Thermoelasticity without energy dissipation for dipolar bodies. Once we get an a priori estimate for the amplitude of the vibration, which are assumed being harmonic in time, it is possible to predict some spatial decay or growth properties for the amplitude, provided the frequency of vibration is greater than a certain critical value.

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Section: Preliminary Resultsmentioning

confidence: 99%

Section: Basic Equationsmentioning

confidence: 99%

Section: Basic Equationsmentioning

confidence: 99%

“…The theory without energy dissipation proposed in Ciarletta [4] allows propagation of thermal waves at a finite speed.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Evolution of solutions for dipolar bodies in Thermoelasticity without energy dissipation

Marín

Abbas

2016

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…The nature of these three types of constitutive functions [8] is that when the respective theories are linearized, model I theory is the same as the classic heat conduction theory (based on Fourier's law); model II theory predicts a finite speed for heat propagation and involves no energy dissipation, now referred to as thermoelasticity without energy dissipation; model III theory permits propagation of thermal signals at both finite and infinite speeds and there is a structural difference between these field equations and those developed in [5,6,10,11]. Ciarletta [3] later formulated a theory of micropolar thermoelasticity without energy dissipation. Detailed and comprehensive references to the developments of generalized thermoelasticity are found in two nice review papers by Chandrasekharaiah [1,2].…”

Section: Introductionmentioning

confidence: 99%

Thermoelasticity without energy dissipation for initially stressed bodies

Wang

Slattery

2002

International Journal of Mathematics and Mathematical Sciences

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Thermoelastic equations without energy dissipation are formulated for a body which has previously received a large deformation and is at nonuniform temperature. A linear theory of thermoelasticity without energy dissipation for prestressed bodies is derived and the uniqueness theorem for a class of mixed initial-boundary value problems is established.2000 Mathematics Subject Classification: 35L90, 74A15, 80A17.1. Introduction. The so-called second sound effect has been given increasing attention in recent decades. This effect arises from the possible transport of heat by a wave propagation process rather than diffusion. Many articles have been devoted to the development of the generalized theory of thermoelasticity that predicts a finite speed for heat propagation. Lord and Shulman [11], employing a modified Fourier's law, developed what now is known as extended thermoelasticity. Green and Lindsay [6], based on an entropy production inequality proposed by Green and Laws [5], formulated temperature-rate dependent thermoelasticity that includes the temperature-rate among constitutive variables. Lebon [10] formulated heat-flux dependent thermoelasticity on the basis of a nonclassical approach to thermodynamics which includes the heat flux among the constitutive variables and assumes an equation of evolution for the heat flux. All these theories yield governing systems of hyperbolic equations and predict finite speed for heat propagation.Recently, Green and Naghdi [7] reexamined the basic postulates of thermomechanics. They postulated three types of constitutive repose functions for the thermal phenomena and, accordingly, formulated three models of thermoelasticity. The nature of these three types of constitutive functions [8] is that when the respective theories are linearized, model I theory is the same as the classic heat conduction theory (based on Fourier's law); model II theory predicts a finite speed for heat propagation and involves no energy dissipation, now referred to as thermoelasticity without energy dissipation; model III theory permits propagation of thermal signals at both finite and infinite speeds and there is a structural difference between these field equations and those developed in [5,6,10,11]. Ciarletta [3] later formulated a theory of micropolar thermoelasticity without energy dissipation. Detailed and comprehensive references to the developments of generalized thermoelasticity are found in two nice review papers by Chandrasekharaiah [1,2].In this paper, we adapt the postulates made by Green and Naghdi [7] and formulate a thermoelasticity theory without energy dissipation for solids which have previously

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Electromagnetic field and three‐phase lag in a compressed rotating isotropic homogeneous micropolar thermo‐viscoelastic half‐space

Bayones

Abo‐Dahab

Abd-Alla

et al. 2021

Math Methods in App Sciences

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Using a thermal shock of the ramp type, the authors constructed a unique mathematical three‐phase‐lag scheme in a compressed rotating isotropic homogeneous micropolar thermo‐viscoelastic medium. The model is applied to solve an issue of an exactly performing half‐space exposed to defined boundary circumstances with an electromagnetic field. Normal mode analysis and Lame's potentials methods were used to obtain the analytical answers. The authors were interested in studying the effect of the initial stress, ramp time, magnetic field, and rotation on distributing, displacement, temperature, and stress, as well as induced electric and magnetic distribution. The findings showed that the impact of the viscous, ramp parameter, rotation, phase lag, magnetic field, and initial stress on the micropolar thermo‐viscoelastic medium is distinct.

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A Theory of Micropolar Thermoelasticity Without Energy Dissipation

Cited by 69 publications

References 0 publications

Evolution of solutions for dipolar bodies in Thermoelasticity without energy dissipation

Evolution of solutions for dipolar bodies in Thermoelasticity without energy dissipation

Thermoelasticity without energy dissipation for initially stressed bodies

Electromagnetic field and three‐phase lag in a compressed rotating isotropic homogeneous micropolar thermo‐viscoelastic half‐space

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