Search results

The thermo-diffusion analysis of an isotropic cylinder under thermal flux and chemical potential impacts has been discussed. Improvements of Green and Naghdi generalized thermoelasticity theory have been proposed.

Some models with and without energy dissipation have been presented as well as the simple forms of Green–Naghdi (G–N) theories. These novel multi- and single-/dual-phase-lag models are presented to investigate the thermo-diffusion of the solid cylinder. The closed-form solution of thermo-diffusion governing equations of solid cylinder has been obtained to deduce all field variables.

A comparison study between the simple G–N II and III models and their improved models has been presented. The validations of outcomes are acceptable and so benchmarks are reported to help other investigators in their future comparisons.

The modified Green and Naghdi theories of types II and III are presented to get novel and accurate models of single- and dual-phase-lag of multiterms. The heat of mass diffusion equation as well as the constitutive equations for the stresses and chemical potential of a solid cylinder is added to the present formulation. The system of three differential coupled equations is solved, and all field variables are obtained for the thermal diffusion of the solid cylinder. Some validation examples and applications are presented to compare the simple and modified Green and Naghdi theories of types II and III. Sample plots are illustrated along the radial direction of the solid cylinder. Some results are tabulated to serve as benchmark results for future comparisons with other investigators. The reported and illustrated results show that the simple G–N II and III models yield the largest values of all field quantities. The single-phase-lag models give the smallest values. However, the dual-phase-lag model yields results that are intermediate between those of the simple and single-phase-lag G–N models.

widely‐used hypoelastic model for four well‐known objective stress rates under a four‐phase stress cycle associated with axial tension and/or torsion of thin‐walled cylindrical tubes. Here, two kinds of models based upon the Cauchy stress and the Kirchhoff stress will be treated. The reduced systems of differential equations of these rate constitutive equations are derived and studied for Jaumann, Green‐ Naghdi, logarithmic and Truesdell stress rates, separately. Analytical solutions in some cases and numerical solutions in all cases are obtained using these reduced systems. Comparisons between the residual deformations are made for different cases. It may be seen that only the logarithmic stress rate results in no residual deformation. In particular, results indicate that Green‐Naghdi rate would generate unexpected residual deformation effect that is essentially different from that resulting from Jaumann rate. On the other hand, it is realized that this study accomplishes an alternative, direct proof for the nonintegrability problem of Truesdell’s hypoelastic rate equation with classical stress rates. This problem has been first treated successfully by Simo and Pister in 1984 using Bernstein’s integrability conditions. However, such treatment needs to cope with a coupled system of nonlinear partial differential equations in Cauchy stress. Here, a different idea is used. It is noted that every integrable hypoelastic equation is just an equivalent rate form of an elastic equation and hence should produce no residual deformations under every possible stress cycle. Accordingly, a hypoelastic model with a stress rate has to be non‐integrable, whenever a stress cycle can be found under which this model generates residual deformation. According to this idea of reductio ad absurdum, a well‐designed stress cycle is introduced and the corresponding residual deformations are calculated. Unlike the treatment of Bernstein’s integrability conditions, it may be a simple and straightforward matter to calculate the final deformations for a given stress cycle. This has been done in this study for several well‐known stress rates.

The purpose of this paper is to study a model of the equations of a two-dimensional problem in a half space, whose surface in a free micropolar thermoelastic medium possesses cubic symmetry as a result of inclined load. The problem is formulated in the context of Green-Naghdi theory of type II (G-N II) (without energy dissipation) and of type III (G-N III) (with energy dissipation) under the effect of magnetic field.

The normal mode analysis is used to obtain the exact expressions of the physical quantities.

The numerical results are given and presented graphically when the inclined load and magnetic field are applied. Comparisons are made with the results predicted by G-N theory of both types II and III in the presence and absence of the magnetic field and for different values of the angle of inclination.

In the present work, the authors study the influence of inclined load and magnetic field in a micropolar thermoelastic medium in the context of the G-N theory of both types II and III. Numerical results for the field quantities are obtained and represented graphically.

The purpose of this paper is to investigate the influence of the gravity and the magnetic fields on the plane waves in a homogenous, linear and isotropic thermoelastic medium subjected to the laser pulse heating.

The problem has been solved analytically and numerically by using the normal mode analysis.

Numerical results for the temperature, the displacement components, the stress components and the volume fraction were presented graphically and analyzed the results. The graphical results indicate that the effect of gravity and magnetic fields are observable physical effects on the porous thermoelastic material heated by a laser pulse. Comparisons are made with the results in the absence and presence of the gravity and the magnetic fields, also at various times.

In the present work, the authors shall formulate a 2-D problem for the propagation of plane waves on the porous thermoelastic material influenced by the gravity and the magnetic fields subjected to a laser pulse heating act as a thermal shock. A comparison is also made between the two types II and III of Green-Naghdi theory in the absence and the presence of the gravity and the magnetic fields. Such problems are very important in many dynamical systems.

The purpose of this paper is to study the effect of rotation and initial stress on magneto-thermoelastic material with voids heated by a laser pulse heating.

The analytical method used was the normal mode analysis technique.

Numerical results for the physical quantities were presented graphically and analyzed. The graphical results indicate that the effect of rotation, initial stress and magnetic fields are observable physical effects on the thermoelastic material with voids heated by a laser pulse. Comparisons are made with the results in the absence and the presence of the physical operators, also at various times.

In the present work, the authors shall investigate the effect of the rotation, initial stress, magnetic field and laser pulse on thermoelastic material with voids subjected to a laser pulse heating acting as a thermal shock. A comparison is also made between the two types (types II and III) of Green-Naghdi theory in the absence and the presence of the physical operators. Such problems are very important in many dynamical systems.

The purpose of this paper is to study the deformation of Green‐Naghdi (type III) thermoelastic solid half‐space under hydrostatic initial stress and rotation.

The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress and temperature distribution.

The numerical results are given and presented graphically when mechanical/thermal source is applied.

Comparisons are made in the presence and absence of hydrostatic initial stress and rotation and their effect is shown graphically.

The purpose of this paper is to study the effect of gravity on the general model of the equations of generalized magneto‐thermo‐microstretch for a homogeneous isotropic elastic half‐space solid whose surface is subjected to a mode‐I crack. The problem is in the context of the Green and Naghdi theory of both types (II and III).

The normal mode analysis is used to obtain the expressions for the displacement components, the force stresses, the temperature, the couple stress and the microstress distribution.

The variations in variables against distance components are given graphically in 2D and 3D.

The linear theory of elasticity is of paramount importance in the stress analysis of steel, which is the commonest engineering structural material. To a lesser extent, the linear elasticity describes the mechanical behavior of the other common solid materials, e.g. concrete, wood and coal. However, the theory does not apply to the behavior of many of the newly synthetic materials of the elastomer and polymer type, e.g. polymethyl‐methacrylate (Perspex), polyethylene and polyvinyl chloride.

Comparisons are made with the results in the presence and absence of gravity and initially applied magnetic field with two cases: the first for the generalized micropolar thermoelasticity elastic medium (without stretch constants) between both types (II, III); and the second for the generalized magneto‐thermoelastic medium with stretch (without micropolar constants) between both types (II, III).

In the present paper, the three-phase-lag (3PHL) model, Green-Naghdi theory without energy dissipation (G-N II) and Green-Naghdi theory with energy dissipation (G-N III) are used to study the influence of the gravity field on a two-temperature fiber-reinforced thermoelastic medium.

The analytical expressions for the displacement components, the force stresses, the thermodynamic temperature and the conductive temperature are obtained in the physical domain by using normal mode analysis.

The variations of the considered variables with the horizontal distance are illustrated graphically. Some comparisons of the thermo-physical quantities are shown in the figures to study the effect of the gravity, the two-temperature parameter and the reinforcement. Also, the effect of time on the physical fields is observed.

To the best of the author’s knowledge, this model is a novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium, and gravity plays an important role in the wave propagation of the field quantities. It explains that there are significant differences in the field quantities under the G-N II theory, the G-N III theory and the 3PHL model because of the phase-lag of temperature gradient and the phase-lag of heat flux.

In the present article, the three-phase-lag (3PHL) model and the Green-Naghdi theory of types II, III with memory-dependent derivative is used to study the effect of rotation on a nonlocal porous thermoelastic medium.

In this study normal mode analysis is used to obtain analytical expressions of the physical quantities. The numerical results are given and presented graphically when mechanical force is applied.

The model is illustrated in the context of the Green-Naghdi theory of types II, III and the three-phase lags model. Expressions for the physical quantities are solved by using the normal mode analysis and represented graphically.

Comparisons are made with the results predicted in the absence and presence of the rotation as well as a nonlocal parameter. Also, the comparisons are made with the results of the 3PHL model for different values of time delay.

The purpose of this paper is to study two-dimensional deformations in a nonlocal, homogeneous, isotropic, rotating thermoelastic medium with temperature-dependent properties under the purview of the Green-Naghdi model II of generalized thermoelasticity. The formulation is subjected to a mechanical load.

The normal mode analysis technique is adopted to procure the exact solution of the problem.

For isothermal and insulated boundaries, discussions have been made to highlight the influences of rotational speed, nonlocality, temperature-dependent properties and time on the physical quantities.

The exact expressions for the displacement components, stresses and temperature field are obtained in the physical domain. These are also calculated numerically for a magnesium crystal-like material and depicted through graphs to observe the variations of the considered physical quantities. The present study is useful and valuable for the analysis of problems involving mechanical shock, rotational speed, nonlocal parameter, temperature-dependent properties and elastic deformation.