Isotropic Thermoelastic Medium Research Articles

Thermoelastic diffusion based on a nonlocal three-phase-lag diffusion model with double porosity structure

This work aims to develop a new diffusion-elasticity-based model using Eringen’s nonlocal elasticity theory under the purview of the three-phase-lag (TPL) model of hyperbolic thermoelasticity. This problem is treated in the context of a double porosity structure in a homogeneous, isotropic thermoelastic medium. By considering the phase laggings of the diffusion flux vector and using nonlocal continuum mechanics, new constitutive and field equations are derived. The problem is solved by employing the normal mode analysis technique which gives the exact results of all the physical variables. To illustrate the theoretical results, different physical quantities are calculated numerically and presented graphically with respect to distance and time. The influences of different thermoelastic models like TPL (three-phase-lag model), GN-III (Green-naghdi model), DPL (dual-phase-lag model), LS (Lord-Shulman model), and CT (coupled thermoelasticity) on the physical quantities are shown graphically. Additionally, the effects of nonlocal parameters, double voids, and diffusion on the physical quantities are represented graphically. Some limiting and particular cases are also derived from the governing equations and those results have been compared with the existing results available in the literature. Some 3D surface curves are also presented to study the impact of diffusion, nonlocality, and double voids on various physical quantities.

Effect of three-phase-lag thermal and three-phase-lag diffusion models on waves at the boundary of elastic and thermoelastic diffusion medium

In this paper, we discuss the reflection and refraction of an incident P wave or [Formula: see text] wave at the interface of a plane. The plane, which is divided into two halves, is an elastic medium [Formula: see text] having an incident wave and a thermoelastic diffusion medium [Formula: see text] with TPLT (i.e., three-phase-lag thermal) and TPLD (i.e., three-phase-lag diffusion) models. It has been noticed that two waves are reflected and four are refracted in an isotropic thermoelastic diffusion medium. Out of the four refracted waves, three are longitudinal waves: a quasi-longitudinal wave [Formula: see text] a quasi-mass diffusion wave [Formula: see text], a quasi-thermal wave [Formula: see text] and one is a transverse wave [Formula: see text]. If we consider the above waves first, the amplitude and energy ratio are calculated by using the surface boundary conditions and then graphically represented to compare the change in energy and amplitude ratio with the change in incident angle for three particular cases. The conservation of energy is depicted by verifying that all the energy sums up to unity. The considered problem has its application in earthquake engineering, astronautics, rocket engineering, seismology and many more engineering areas.

Laser-Induced Thermoelastic Response in an Isotropic Medium Having Variable Material Moduli

Thermal displacement and stress distribution are analysed in the domain of plane-strain geometry of an isotropic thermoelastic medium having variable material moduli. In this context of the analysis, laser induced heat sources are planted on the reference plane. To analyse the thermal responses due to the injected heat sources into the medium, hyperbolic type heat conduction model with three phase-lags incorporated. Analytical solutions are expressed in-terms of Laplace–Fourier integral transform domain and the physical behaviour of displacement and stresses are depicted through a discretised form of inverse-integral transformation technique. Finally, parameterized characteristic analysis are presented graphically and the salient features of thermal displacements are highlighted.

Submodels of the model of dynamic deformation of a transversally isotropic thermoelastic medium for solving the problems of horizontal crack formation at 3D printing

Submodels of the model of dynamic deformation of a transversally isotropic thermoelastic medium for solving the problems of horizontal crack formation at 3D printing

Propagation of plane waves in a nonlocal transversely isotropic thermoelastic medium with voids and rotation

AbstractThe objective of present research work is to investigate the propagation of time harmonic plane waves in a rotating, nonlocal, transversely isotropic thermoelastic half‐space having void pores in the context of Lord–Shulman theory. It has been observed that four coupled plane waves travel in such type of medium with distinct speeds. Using appropriate boundary conditions, the amplitude and energy ratios for the reflected waves are presented. Numerical computations for a magnesium crystal‐like material are performed with the help of MATLAB software to study the effects of material anisotropy, nonlocal, void and rotation parameters on the amplitude ratios. The computational results are displayed and explained through graphs. The phase velocities of plane waves in transversely isotropic medium are found to depend upon the incident angle, whereas these attain constant values in an isotropic medium. The energy conservation law is also justified during the reflection phenomena.

Reflection of plane waves in a rotating nonlocal fiber-reinforced transversely isotropic thermoelastic medium

The present investigation is concerned with the reflection of plane waves from the free surface of a rotating nonlocal, fiber-reinforced, transversely isotropic thermoelastic medium in the context of Lord-Shulman theory. It has been observed that three coupled plane waves travel in the medium with distinct speeds. Using appropriate boundary conditions, the amplitude ratios for the reflected waves are derived and the numerical computations have been carried out using MATLAB software. The modulus of amplitude ratios is presented graphically to exhibit the effects due to presence of fiber-reinforcement, nonlocal and rotation parameters. The expressions of energy ratios have also been derived in explicit form and are portrayed graphically as functions of angle of incidence. The phase velocities of plane waves in transversely isotropic medium are found to depend upon the incident angle, whereas these attain constant values in isotropic medium. The energy conservation law is also justified during the reflection phenomena.

State space approach to study thermal shock problem in nonlocal thermoelastic medium with double porosity

In this article, a two-dimensional problem is studied in a homogeneous isotropic thermoelastic medium with double porosity in the context of nonlocal thermoelasticity and the problem is treated in the presence of the Green–Naghdi model of type-III. Constitutive relations and field equations are derived and the state space approach is employed to solve this problem. Thermal shock is applied on the boundary of the surface. From these relations and expressions, we have calculated stress components, displacement components, and temperature for different values of distance and time numerically and plotted graphically to demonstrate and compare theoretical results. The influences of void parameters, locality, and nonlocality on the various physical quantities are also analyzed. Some particular and special cases are also deduced from this study and compared with the existing results.

Magnetic-thermal-elastic waves under the impact of induced laser pulses and hyperbolic two temperature theory with memory-dependent derivatives (MDD)

A novel model with theoretical investigations of generalized hyperbolic two-temperature theory in the context of the generalized thermoelasticity theory is studied. The elastic medium is excited at the outer surface by an external magnetic field and pulsed laser. The model is established in the context of the memory-depended derivative (MDD) when the elastic material time-dependent. The governing equations describe the interaction processes for isotropic homogeneous hyperbolic thermoelastic elastic medium in one-dimensional (1D) deformation when the non-Gaussian laser pulse model is applied with time delay. The Laplace transform is used to obtain the analytical solutions of the main physical fields. The medium is loaded when a traction is free and thermally shocked with time-dependent. The complete solutions are obtained in the Laplace time domain when used the inverse of Laplace transform numerically. Numerical results of the main physical quantities are discussed graphically under the effect of hyperbolic two-temperature, magnetic field and laser pulses when the time-delay parameter is taken into consideration.

Thermo-mechanical interactions in a nonlocal transversely isotropic material with rotation under Lord–Shulman model

The objective of this manuscript is to examine the thermodynamical disturbances in a rotating nonlocal transversely isotropic thermoelastic solid half-space. The enunciation is applied to Lord–Shulman model of generalized thermoelasticity with Eringen's nonlocal elasticity theory. The formulation is subjected to a mechanical load. The expressions for the displacement components, stresses and temperature field are obtained by using normal mode technique and the numerical computations have been carried out with the help of MATLAB software for zinc crystal-like material. The comparisons are made among the results obtained by taking into account the different values of rotation parameter ( Ω = 0.0 , 0.1 , 0.3 ) , nonlocal parameter ( ε = 0.195 × 10 − 9 , 0.195 × 10 − 4 , 0.195 × 10 − 1 ) and time ( t = 0.1 , 0.3 , 0.5 ) . The outcomes point out a strong impact of the rotation, nonlocality and time on the physical quantities and agree with the boundary conditions. Although various studies exist in the literature for local and isotropic thermoelastic medium, but the current results are presented in an anisotropic and nonlocal thermoelastic rotating medium, which have not been studied so far.

On propagation of harmonic plane waves under the Moore–Gibson–Thompson thermoelasticity theory

ABSTRACT The present work is aimed at a detailed investigation of harmonic plane wave propagation through an isotropic, unbounded and homogeneous thermoelastic medium under the recently proposed Moore–Gibson–Thompson (MGT) thermoelasticity theory. The dispersion relation is derived and its solution for the longitudinal plane wave propagation is obtained analytically. Two different modes of longitudinal wave are identified as elastic and thermal mode waves. The asymptotic expressions of various important characteristics of the wave fields such as phase velocity, specific loss and penetration depth for both the waves are obtained for limiting cases of very high and low frequency values. The Whitham stability of harmonic plane waves is established. Further, the computational tool is used to achieve numerical results for these wave characteristics and to illustrate the analytical findings graphically. Some important observations about the prediction of the MGT model in comparison to the other existing models, i.e. classical coupled thermoelastic model, LS model and GN-III model, are highlighted. Effects of material parameters on the propagation of waves are analyzed in a detailed manner. From the theoretical as well as numerical results, it is investigated that the MGT model accounts for finite speed of elastic wave as well as thermal wave.

Waves in thermoelastic solid half‐space containing voids with liquid loadings

AbstractThe influence of the voids in the propagation of time‐harmonic plane waves in a semi‐infinite homogeneous isotropic thermoelastic medium in contact with inviscid liquid half‐space has been explored under the Lord‐Shulman theory of thermoelasticity. The incompressible and non‐viscous liquid is taken in the upper half‐space and the effect of gravity on the whole system is assumed to be negligible. The mathematical model is developed and the exact expressions for the considered variables are obtained by using the normal mode analysis method. The compact secular equation for the considered model is derived for thermally insulated and isothermal cases respectively. There exist four waves in the generalized thermoelastic porous solid half‐space and one wave exists in the liquid half‐space. In the solid half‐space, one is a transverse wave and the remaining three is the set of coupled dilatational waves. The coupling among these waves is because of the presence of voids and thermal effects, also the amplitude of oscillation of these waves decreases with time. The transverse wave in the solid half‐space is undamped in time and remains independent of the effects of voids and heat. The particle's motion is deduced for Rayleigh wave propagation and found to be elliptical in solid half‐space and circular in liquid half‐space. Also, the plane of particle motion is tilted due to the presence of void parameters in the medium. Magnesium crystal has been chosen for the numerical computation and the discussion of various graphs depicting the profiles are presented in the last section.

Fractional order heat conduction and thermoelastic response of a thermally sensitive rectangular parallelopiped

In the present paper, the problem of finite dimensional rectangular parallelepiped in isotropic thermoelastic medium with convective type heating is considered. The heat conduction equation (HCE) of the region is described by time HC of fractional order with Caputo derivative form. The non-linear form of heat conduction equation is converted to linear form with Kirchhoff’s transformation. Integral transform technique is used to deal with the spatial variables and Laplace transform technique is used to deal with Caputo type time fractional derivative. Inverse Laplace transform and inverse finite Fourier transform are employed to expose the solution in the transformed domain. Numerical results are obtained for temperature distribution, deflection, stress resultants and thermal stress distribution for different values of time fractional order parameter. These results are presented graphically and discussed for various values of time fractional parameters. The obtained results show significant influence of the time fractional order derivative on the temperature as well as stress distribution. Thermosensitivity plays a vital role in the analysis of any real thermoelastic problems and one should consider their effect while dealing with materials in high temperature environment.

Three-dimensional quasi-static general solution for isotropic thermoelastic medium with applications

An accurate and efficient method for three dimensional quasi-static thermal elastic problems is established. The three-dimensional equations of isotropic quasi-static-thermo-elasticity are simplified by the introduction of two displacement functions. A general solution is derived by virtue of the Almansi's theorem, which is expressed in terms of three functions, satisfying harmonic functions and quasi-static heat conduction equation respectively. Exact and complete fundamental solution would be derived for arbitrary boundary problems subjected to a point heat load. The solution is concise in form which is completely new to the literature. In this paper, the 3D solutions of the isotropic quasi-static medium under dynamic point heat source based on the general solutions are presented by two newly functions. All components of the coupled field are expressed in terms of elementary functions which are convenient to use. The number results for two types of dynamic heat source show the change rules of the thermal stress field. The corresponding analysis can give some theoretical basis for revealing the mechanism of thermal elastic coupling problem and provide guidance for engineering structural design in the future work.

Thermoelastic Rayleigh wave: explicit expression for complex velocity

Propagation of Rayleigh waves is considered in an isotropic thermoelastic semi-infinite medium with isothermal or insulated boundary. This requires to solve an irrational complex equation for an implicit complex velocity. A complex analysis technique is used to solve this implicit equation so as to derive an explicit expression for the velocity of the Rayleigh wave in thermoelastic materials. The same expression allows calculation of the velocity of Rayleigh wave in thermo-viscoelastic medium as well.

Study of frequency shift and thermoelastic damping in transversely isotropic nano-beam with GN III theory and two temperature

In this study, a nanoscale beam of transversely isotropic thermoelastic (TIT) medium with two temperature and with Green–Naghdi (GN) III theory of thermoelasticity for free vibrations with simply supported boundaries have been examined. Euler–Bernoulli (EB) beam theory is used to formulate a mathematical model of the nanoscale beam in a closed form. The lateral deflection, frequency shift, thermal moment and thermoelastic damping have been solved. A program in MATLAB software is developed to find the numerical values for different physical quantities. The lateral deflection, frequency shift, thermal moment and thermoelastic damping for the varying two temperature, different modes, frequency of time harmonic sources, thickness of nano-beam, and material medium of nano-beam has been represented graphically and discussed. The results for some particular cases have also been compared to some earlier work done.

The effect of multi-phase-lag and Coriolis acceleration on a fiber-reinforced isotropic thermoelastic medium

The three-phase-lag model, thermoelasticity without energy dissipation (G-N II) theory and thermoelasticity with energy dissipation (G-N III) theory are applied to study the effect of rotation on a fiber-reinforced thermoelastic medium. The exact expressions for the physical quantities were obtained by using the normal mode analysis. The numerical results for the field quantities are given in the physical domain and illustrated graphically in the absence and presence of rotation, Coriolis acceleration as well as reinforcement parameters.

Transient disturbances in a nonlocal functionally graded thermoelastic solid under Green–Lindsay model

PurposeThe purpose of this study is to analyze the two-dimensional disturbances in a nonlocal, functionally graded, isotropic thermoelastic medium under the purview of the Green–Lindsay model of generalized thermoelasticity. The formulation is subjected to a mechanical load. All the thermomechanical properties of the solid are assumed to vary exponentially with the position.Design/methodology/approachNormal mode technique is proposed to obtain the exact expressions for the displacement components, stresses and temperature field.FindingsNumerical computations have been carried out with the help of MATLAB software and the results are illustrated graphically. These are also calculated numerically for a magnesium crystal-like material and illustrated through graphs. Theoretical and numerical results demonstrate that the nonlocality and nonhomogeneity parameters have significant effects on the considered physical fields.Originality/valueInfluences of nonlocality and nonhomogeneity on the physical quantities are carefully analyzed for isothermal and insulated boundaries. The present work is useful and valuable for analysis of problems involving mechanical shock, nonlocal parameter, functionally graded materials and elastic deformation.

Surface waves in porous thermoelastic medium with two relaxation times

In this paper, the propagation of Rayleigh waves in homogeneous isotropic thermoelastic medium in the presence of voids with Green-Lindsay model is considered. A vector matrix differential equation is formed by employing normal mode analysis to the considered equations which is then solved by eigenfunction expansion method. The frequency equations for different cases are derived and the path of surface particles during Rayleigh wave propagation is found elliptical. The phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and presented graphically and the effect of the voids on the considered parameters is shown in the figures.

Elasto-thermodiffusive interaction subjected to rectangular thermal pulse and time-dependent chemical shock due to Caputo-Fabrizio heat transfer

This present work is devoted to investigate the transient phenomena for a novel mathematical model of elasto-thermodiffusion in an isotropic three-dimensional thermoelastic medium subjected to permeating gas induced by a rectangular thermal pulse, where the heat conduction equation is defined in an integral form of a common derivative involving a nonsingular kernel interval by incorporating the Caputo-Fabrizio (CF) heat transfer law. The time-dependent chemical potential is also assumed to be known on the bounding plane. Employing the Laplace transform and double-Fourier transform techniques, the problem has been solved analytically in the transformed domain. Numerical inversion of the Laplace transform and double-Fourier transforms are carried out using a Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Excellent predictive capability is demonstrated due to the presence of the CF parameter and thermodiffusion also.

Temperature-Rate-Dependent Thermoelasticity Theory With Memory-Dependent Derivative: Energy, Uniqueness Theorems, and Variational Principle

Abstract This article is focused on developing a new mathematical model on the temperature-rate-dependent thermoelasticity theory (Green–Lindsay), using the methodology of memory-dependent derivative (MDD). First, the energy theorem of this model associated with two relaxation times in the context of MDD is derived for homogeneous, isotropic thermoelastic medium. Second, a uniqueness theorem for this model is proved using the Laplace transform technique. A variational principle for this model is also established. Finally, the results for Green–Lindsay model without MDD and coupled theory are obtained from the considered model.