Theory Of Micropolar Thermoelasticity Research Articles

Application of the fractional-order theory of micropolar thermoelasticity in the solid cylinder

Application of the fractional-order theory of micropolar thermoelasticity in the solid cylinder

Thermoelastic Plane Waves in Materials with a Microstructure Based on Micropolar Thermoelasticity with Two Temperature and Higher Order Time Derivatives

The study of the effect of the microstructure is important and is most evident in elastic vibrations of high frequency and short-wave duration. In addition to deformation caused by temperature and acting forces, the theory of micropolar thermoelasticity is applied to investigate the microstructure of materials when the vibration of their atoms or molecules is increased. This paper addresses a two-dimensional problem involving a thermoelastic micro-polar half-space with a traction-free surface and a known conductive temperature at the medium surface. The problem is treated in the framework of the concept of two-temperature thermoelasticity with a higher-order time derivative and phase delays, which takes into consideration the impact of microscopic structures in non-simple materials. The normal mode technique was applied to find the analytical formulas for thermal stresses, displacements, micro-rotation, temperature changes, and coupled stress. The numerical results are graphed, and the effect of the discrepancy indicator and higher-order temporal derivatives is examined. There are also some exceptional cases that are covered.

Reflection of coupled dilatational and shear waves in the generalized micropolar thermoelastic materials

The problem of wave propagation in the generalized theory of micropolar thermoelasticity under the Green–Lindsay model has been investigated. We have investigated the reflected dilatational and shear waves due to incident waves at a plane-free surface of generalized micropolar thermoelastic materials. The amplitude and energy ratios corresponding to the reflected coupled dilatational and coupled shear waves are derived using boundary conditions at the free surface. These ratios are also computed numerically for a particular model. Note that there are critical angles for the incident shear wave.

Fundamental solution of steady oscillations for porous materials with dual-phase-lag model in micropolar thermoelasticity

This article deals with the study of propagation of plane waves in an isotropic thermoelastic medium for porous materials with the linear theory of micropolar thermoelasticity. The problem is treated in the context of dual-phase-lag model of thermoelasticity. It is found that, for one-dimensional model, there exists three longitudinal waves, namely elastic (E-mode), thermal (T-mode), and volume fraction (V-mode) in addition to transverse waves which get decoupled from rest of the motion and not affected by thermal and volume fraction fields. In case of steady oscillations, the fundamental solution of the system of differential equations in terms of elementary functions has been constructed. The phase velocity and attenuation coefficient of these waves are computed numerically and presented graphically.

Eigenvalue formulation to micropolar porous thermoelastic circular plate using dual phase lag model

PurposeThe purpose of this paper is to study the axisymmetric problem in a micropolar porous thermoelastic circular plate with dual phase lag model by employing eigenvalue approach subjected to thermomechanical sources.Design/methodology/approachThe Laplace and Hankel transforms are employed to obtain the expressions for displacements, microrotation, volume fraction field, temperature distribution and stresses in the transformed domain. A numerical inversion technique has been carried out to obtain the resulting quantities in the physical domain. Effect of porosity and phase lag on the resulting quantities has been presented graphically. The results obtained for Lord Shulman theory (L-S, 1967) and coupled theory of thermoelasticity are presented as the particular cases.FindingsThe variation of temperature distribution is similar for micropolar thermoelastic with dual (MTD) phase lag model and coupled theory of thermoelasticity. The variation is also similar for tangential couple stress for MTD and L-S theory but opposite to couple theory. The behavior of volume fraction field and tangential couple stress for L-S theory and coupled theory are observed opposite. The values of all the resulting quantities are close to each other away from the sources. The variation in tangential stress, tangential couple stress and temperature distribution is more uniform.Originality/valueThe results are original and new because the authors presented an eigenvalue approach for two dimensional problem of micropolar porous thermoelastic circular plate with dual phase lag model. A comparison of porosity, L-S theory and coupled theory of micropolar thermoelasticity is made. Such problem has applications in material science, industries and earthquake problems.

On a Physical Field Theory of Micropolar Thermoelasticity

A non-linear mathematical model of thermoelastic micropolar continuum is developed. The model is presented in terms of 4-covariant field theoretical formalism. Lagrangian density for thermoelastic continuum with three micropolar directors is given and the least action principle is formulated. Corresponding field equations of micropolar thermoelasticity are obtained. Variational symmetries of the thermoelastic action are used to formulate covariant conservation laws. Following the usual procedure, micropolar thermoelastic Lagrangians are represented as functions of independent rotationally invariant arguments. The latter constitutes a complete system of objective finite strain measures of micropolar thermoelasticity. Constitutive equations of micropolar thermoelasticity are obtained and discussed.

Analytical Aspects in the Theory of Thermoelastic Bodies with Microstructure and Two Temperatures

In the present work, some essential theorems on the linear coupled theory of micropolar thermoelasticity with two temperatures are established. The uniqueness theorem is proved in two distinct approaches without the positive definiteness assumptions on the thermoelastic modulus. The reciprocity theorem is established by the aid of an integral identity that involves two admissible processes at two different instants. The continuous dependence results on the external data are studied. The variational principle of Gurtin type is established. Finally, we solve the problems of concentrated heat source and body force to study the effect of two-temperature influence on the relevant variables.

Plane waves and vibrations in the theory of micropolar thermoelasticity for materials with voids

The present paper concerns with the linear theory of micropolar thermoelasticity for materials with voids. Some basic properties of wave numbers of the longitudinal and transverse plane harmonic waves are treated. The existence theorems of non-trivial solutions and eigenfrequencies of the interior homogeneous boundary value problems of steady vibrations are proved. The connection between plane harmonic waves and eigenfrequencies of the aforementioned problems is established.

On representations of a general solution in the theory of micropolar thermoelasticity without energy dissipation

In the present paper, the linear theory of micropolar thermoelasticity without energy dissipation is considered. This work is organized as follows: Section 2 is devoted to basic equations for micropolar thermoelastic materials, supposed to be isotropic and homogeneous, and to assumptions on constitutive constants. In Section 3, some theorems related to representations of a general solution are studied.

Fundamental Solution in the Theory of Micropolar Thermoelasticity for Materials with Voids

This paper concerns with the linear theory of micropolar thermoelasticity for materials with voids. We construct the fundamental solution of the system of differential equations in the case of steady oscillations in terms of elementary functions. Some basic properties of this solution are established.

Fundamental Solution in the Theory of Micropolar Thermoelasticity without Energy Dissipation

ABSTRACT This paper concerns the linear theory of micropolar thermoelasticity without energy dissipation. We construct the fundamental solution of the system of differential equations in the case of steady oscillations in terms of elementary functions.

Restudy of coupled field theories for micropolar continua (I)—Micropolar thermoelasticity

Problems of micropolar thermoelasticity have been presented and discussed by some authors in the traditional framework of micropolar continuum field theory. In this paper the theory of micropolar thermoelasticity is restudied. The reason why it was restricted to a linear one is analyzed. The rather general principle of virtual work and the new formulation for the virtual work of internal forces as well as the rather complete Hamilton principle in micropolar thermoelasticity are established. From this new Hamilton principle not only the equations of motion, the balance equation of entropy, the boundary conditions of stress, couple stress and heat, but also the boundary conditions of displacement, microrotation and temperature are simultaneously derived.

A THEORY OF MICROPOLAR THERMOELASTICITY WITHOUT ENERGY DISSIPATION

In this article we use the results of Green and Naghdi Proc. Roy. Soc. London A, vol. 432, pp. 171-194, 1991 and vol. 357, pp. 253-270, 1977 and J. Elasticity, vol. 31, pp. 189-209, 1993] to establish a theory of micropolar thermoelasticity that permits propagation of thermal waves at a finite speed. A solution of Galerkin type for homogeneous and isotropic bodies is also established. This solution is used to study the effect of a concentrated heat source. The continuous dependence of the solution with respect to body loads and initial data is finally studied.

On some theorems in the theory of micropolar thermoelasticity

The paper is concerned with the linear theory of micropolar thermoelasticity. First, we establish a uniqueness theorem with no definiteness assumption on the elasticities and in the absence of restriction that the conductivity tensor is positive definite. Then, we establish a basic relation which implies in a simple way the reciprocal theorem and another uniqueness result.

Heat-flux dependent micropolar thermoelasticity

A theory of micropolar thermoelasticity which includes heat-flux among the constitutive variables is formulated. It is found that the linearized version of the theory admits second-sound effects. An equation of energy balance and a theorem on the uniqueness of solution are deduced for anisotropic materials.

Some applications of micropolar mechanics to earthquake problems

In this paper the theory of micropolar continua has been used to study some earthquake problems. In the first part of the paper the changes in the Earth's inertia tensor due to earthquake faulting are calculated by using a reciprocal relation. The case of a homogeneous and isotropic elastic Earth model is analyzed. The result is compared to that of the classical theory. In the second part of the paper the problem of body loadings equivalent to a seismic dislocation, in the framework of the linear theory of micropolar thermoelasticity, is studied.

PROPAGATION OF MICROPOLAR THERMOELASTIC WAVES IN AN INFINITE ELASTIC SPACE CONTAINING A CYLINDRICAL BORE

The propagation of waves in an infinite micropolar elastic solid containing a cylindrical cavity and under the influence of temperature is investigated. Waves with axial symmetry with respect to the axis of the cavity are discussed, using the linear theory of micropolar thermoelasticity.

Thermal stresses in micropolar elastic cylinders

The present paper is concerned with the static problem in the linear theory of micropolar thermoelasticity for homogeneous and isotropic cylinders. The problem is solved using some results established in [1]–[5].

Thermal stresses in micropolar elastic solids

Two general solutions to the linear theory of micropolar thermoelasticity are presented; one representation involves deformation potentials, the other employs stress-functions. The two representations are used to analyze the thermal stresses and thermal couple stresses in the vicinity of a cavity and a rigid inclusion during uniform heat flow.

On thermal stresses in plane strain of isotropic micropolar elastic solids

We consider the static problem of plane strain in the linear theory of micropolar thermoelasticity assuming that heat sources are absent. We give a method for the reduction of the thermoelastic problem to an isothermal one with certain known boundary conditions. In the case of a multiply connected region this leads to the notion of dislocations.