Temperature-rate Dependent Thermoelasticity Research Articles

Memory-dependent generalized thermoelasticity with finite wave speeds

The present article deals with the question: how time dependent non-locality influence the domain of dependency of thermal signals in solids? In order to establish the hypothesis “domain of influence” in an isotropic medium, based on the temperature-rate dependent thermoelasticity (TRDTE) theory, a thermodynamic consistent model is formulated by incorporating memory-dependent derivative (MDD). Firstly, the domain of influence theorem is established followed by a domain of dependence inequality and it certifies that for a finite time t>0 a solution of a given thermo-dynamical problem, corresponding to the data defined in a bounded support, vanishes outside a suitably defined bounded domain D*(t). It physically interprets that an initial perturbation of a bounded thermo-elastic domain generates thermal signals which for any t>0 can not occupy the whole space, i.e. it propagates with a finite speed. Finally, a two-dimensional thermoelastic problem in the isotropic medium is considered for a supporting visualization of the domain of influence theorem of the memory-dependent generalized thermoelasticity theory.

On the fundamental solutions for the strain and temperature rate-dependent generalized thermoelasticity theory

The present paper concerns with the fundamental solutions for strain and temperature rate-dependent thermoelasticity theory recently developed by Yu et al. (2018). This recently developed model is theoretically established with the aid of principles of thermodynamics and by adding the strain-rate term in temperature rate-dependent thermoelasticity theory, which was proposed by Green and Lindsay (GL)(1972). This model has attempted to remove the drawback of discontinuity in the displacement field under Green-Lindsay (GL) model. We consider this modified Green-Lindsay (MGL) model for the case of homogeneous and isotropic bodies. Two cases, namely, concentrated body force and concentrated heat source have been taken for deriving the fundamental solutions for thermoelasticity in the context of MGL model. The fundamental solutions for the distributions of displacement components and temperature are obtained by the Laplace transform method. Fundamental solutions in the physical domain are obtained by Laplace inversion and the solution of displacement and temperature is obtained for short-time approximation. Lastly, we get the fundamental solution of the system of equations in the case of steady oscillations.

An investigation on strain and temperature rate-dependent thermoelasticity and its infinite speed behavior

The present work is aimed at a mathematical analysis of the newly proposed strain and temperature rate-dependent thermoelasticity theory, also called a modified Green–Lindsay model (MGL) theory, given by Yu et al. (2018). This model is also an attempt to remove the discontinuity in the displacement field observed under temperature rate-dependent thermoelasticity theory proposed by Green and Lindsay. We study thermoelastic interactions in an infinite homogeneous, isotropic elastic medium with a cylindrical cavity based on this model when the surface of the cavity is subjected to thermal shock. The solutions for the distribution of displacement, temperature, and stress components are obtained by using the Laplace transform technique. The inversion of the Laplace transform is carried out by short-time approximation. A detailed comparison of the analytical results predicted by the MGL model with the corresponding predictions by the Lord–Shulman model and the Green–Lindsay model is performed. It is observed that strain rate terms in the constitutive equation avoid the prediction of discontinuity in the displacement field and other significant effects are noted. However, the new theory predicts the infinite speed of disturbance like the classical theory. Variations of field variables at different time are graphically displayed for different models and compared by using a numerical method.

On the Temperature-Rate Dependent Two-Temperature Thermoelasticity Theory

Abstract This work aims to formulate the temperature-rate dependent two-temperature (TRDTT) theory of thermoelasticity. The two-temperature thermoelasticity theory and the temperature-rate dependent thermoelasticity theory are two well-established thermoelasticity theories, which are developed from the generalized thermodynamic principles independently. Although the constitutive equations for TRDTT theory have been introduced, the formulation for the theory from the thermodynamical principles is not yet derived. Therefore, this work is an attempt to establish the theory from the generalized laws of thermodynamics and derive all the governing equations and constitutive relations for the theory. We derive a new and more general two-temperature relation that involves the temperature-rate terms of conductive and thermodynamic temperatures. We observe that this relation is different from the two-temperature relation reported in the literature. Further, we prove the uniqueness of solution for a general mixed initial boundary value problem in the context of linear modified TRDTT thermoelasticity theory for anisotropic medium. To investigate the effect of the present modified TRDTT theory, we solve a one-dimensional half-space problem and highlight the significance of the present theory.

Galerkin-type solution for the theory of strain and temperature rate-dependent thermoelasticity

Ultrafast heating has gained serious attention due to technological advancements in recent years. The thermoelastic process accounting for the finite speed of thermal signals is therefore becoming increasingly important. With the help of extended thermodynamics, Yu et al. (Meccanica 53(10):2543–2554, 2018) have established a thermoelastic model by including the strain rate and temperature rate in the constitutive equations. This model is also an attempt to remove the discontinuity in the displacement field under temperature rate-dependent thermoelasticity theory. The present work seeks to derive the representation of a Galerkin-type solution in the context of this recently proposed model in terms of elementary functions. The representation theorem of the Galerkin-type solution of the system of equations for steady oscillation is also proved. In accordance with this theorem, we finally establish a theorem which expresses the general solution of the system of homogeneous equations of steady oscillation in terms of metaharmonic functions.

Effect of Rotation in an Orthotropic Elastic Slab

The fundamental equations of the two dimensional generalized thermoelasticity (L-S model) with one relaxation time parameter in orthotropic elastic slab has been considered under effect of rotation. The normal mode analysis is used to the basic equations of motion and heat conduction equation. Finally, the resulting equations are written in the form of a vector-matrix differential equation which is then solved by the eigenvalue approach. The field variables in the space time domain are obtained numerically. The results corresponding to the cases of conventional thermoelasticity CTE), extended thermoelasticity (ETE) and temperature rate dependent thermoelasticity (TRDTE) are compared by means of graphs.

Fractional order generalized electro-magneto-thermo-elasticity

Abstract Built upon the fractional order generalized thermoelasticity (FOGTE), which is based on ETE (extended thermoelasticity), a fractional order generalized electro-magneto-thermo-elasticity (FOGEMTE) theory is developed for anisotropic and linearly electro-magneto-thermo-elastic media by introducing the dynamic electro-magnetic fields, with various generalized thermoelasticity considered, such as ETE, TRDTE (temperature rate dependent thermoelasticity), TEWOED (thermoelasticity without energy dissipation), TEWED (thermoelasticity with energy dissipation), DPLTE (dual-phase-lag thermoelasticity). The two temperature (thermodynamics and conductive temperature) model is also introduced. In addition, to numerically deal with the multi-physics problems expressed by a series of partial differential equations especially a fractional one, the corresponding variational principle based on the variational integral method is proposed, and various degenerated variational theorems are presented. A generalized variational theorem is obtained for the unified theory by using the semi-inverse method. Finally, two examples are numerically validated, and concluding remarks are also given.

Fractional Order Generalized Electro-Magneto-Thermo-Elasticity with Magnetic Monopoles and Geometrical Nonlinearity

Recently, Youssef developed the fractional order generalized thermoelasticity (FOGTE) in the context of extended thermoelasticity (ETE). In this work, we extended the concept of fractional calculus into the temperature rate dependent thermoelasticity (TRDTE) and introduced the unified form of the two cases. Upon introducing the electromagnetic field with magnetic monopoles and considering the geometrical nonlinearity, we proposed a fractional order generalized electro-magneto- thermo-elasticity (FOGEMm-poleTEg-non) with magnetic monopoles (m-pole) and geometrical nonlinearity (g-non). To deal with multi-physics problems using numerical methods, we obtained a generalized variational theorem by using the semi-inverse method.

TEMPERATURE RATE DEPENDENT GENERALIZED THERMOELASTICITY WITH MODIFIED OHM'S LAW

The present work is concerned with an electro-magneto-thermoelastic coupled problem for a homogeneous, isotropic, thermally and electrically conducting semi-infinite solid medium in two-dimensional space where an initial magnetic field with constant intensity acts parallel to the plane boundary of the half-space. The surface of the half-space taking as traction free which is subjected to a thermal shock. The modified Ohm's law including the temperature gradient and charge density effect to the governing equations of the generalized thermoelasticity under the temperature rate dependent thermoelasticity (TRDTE) proposed by Green and Lindsay (GL model) has been introduced. Normal mode analysis together with eigenvalue approach technique is used to obtain the general solutions for the physical quantities. Numerical results for the physical quantities are illustrated graphically and analyzed. The graphical results indicate that the effect of the coefficient connecting the temperature gradient and the electric current density of the modified Ohm's law on the plane waves is very pronounced. Comparison are made with the results obtained in the absence of the above coefficient.

Uniqueness and reciprocal theorems in linear micropolar electro-magnetic thermoelasticity with two relaxation times

A general model for the linear micropolar electro-magnetic thermoelastic continuum based on the hyperbolic heat equation, which is physically more relevant than the classical thermoelasticity theory in analyzing problems involving very short intervals of time and/or very high heat fluxes, is introduced. An integral identity that involves two admissible processes at different instants is established. Uniqueness theorem is proved, with no definiteness assumption on the elastic constitutive coefficients and no restrictions on the electro-elastic coupling moduli, magneto-elastic coupling moduli, and thermal coupling coefficients other than symmetry conditions. The reciprocity theorem is derived, without the use of Laplace transforms. The integral representation formula is obtained in case instantaneous concentrated, time-continuous or time-harmonic loads are applied. The Maysel’s, Somigliana’s and Green’s formulas are derived. The mixed boundary value problem is considered and a system of five singular Fredholm integral equations is obtained. The results for dynamic classical coupled theory can be easy deduced from the given general model formulated for the temperature-rate dependent thermoelasticity.

Comments on the articles “Hyperbolic thermoelasticity: A review of recent literature” (Chandrasekharaiah DS, 1998, Appl Mech Rev 51(12), 705–729) and “Thermoelasticity with second sound: A review” (Chandrasekharaiah DS, 1986, Appl Mech Rev 39(3), 355–376)

This review article is a continuation of a previous article by the author, Thermoelasticity with second sound: A review, which appeared in this journal in March, 1986 (Appl Mech Rev39 (3) 355-376). Here, attention is focused on papers published during the past 10-12 years. Contributions to the theory of thermoelasticity with thermal relaxation and the temperature-rate dependent thermoelasticity theory are reviewed. The recently developed theory of thermoelasticity without energy dissipation is described, and its characteristic features highlighted. A glance is made at the new thermoelasticity theory which includes the so-called dual-phase-lag effects. There are 338 references.

Hyperbolic Thermoelasticity: A Review of Recent Literature

This review article is a continuation of a previous article by the author, Thermoelasticity with second sound: A review, which appeared in this journal in March, 1986 (Appl Mech Rev39(3) 355-376). Here, attention is focused on papers published during the past 10-12 years. Contributions to the theory of thermoelasticity with thermal relaxation and the temperature-rate dependent thermoelasticity theory are reviewed. The recently developed theory of thermoelasticity without energy dissipation is described, and its characteristic features highlighted. A glance is made at the new thermoelasticity theory which includes the so-called dual-phase-lag effects. There are 338 references.

Epicentral and near epicenter surface displacements on pulsed laser irradiated metallic surfaces

The elastic deformations associated with the pulsed laser, photothermal heating of an aluminum alloy surface have been measured within the irradiated region using a Michelson-type interferometer. The displacements within this region have been measured and have been compared to calculations based on temperature-rate dependent thermoelasticity theory. The quantitative agreement between calculation and experiment shows the contributions of the local thermal expansion and the propagating acoustic modes on the overall displacements at the epicenter and near the epicenter of the irradiated region. Nonlinear effects on the propagation of the near-field surface acoustic wave may be present.

Spherically symmetric thermoelastic waves in a temperature-rate dependent medium with a spherical cavity

The temperature-rate dependent thermoelasticity theory is employed to study spherically symmetric thermoelastic waves in an infinite medium with a spherical cavity whose inner boundary is subjected to (i) unit-step in temperature change and zero stress and (ii) unit-step in stress and zero temperature change. The effect of thermal relaxation times on the thermoelastic disturbances being short-lived, short-time approximations of the solutions for deformation, temperature and stresses have been considered. It is observed that the temperature and deformation are discontinuous at both the wave fronts while the stresses suffer delta-function singularities in case (i) and in case (ii), the deformation and temperature are continuous at both the wave fronts, while the stresses are discontinuous at these locations.

Radially symmetric temperature-rate dependent thermoelastic wave propagation in an infinitely extended thin plate containing a circular hole

Temperature-rate dependent thermoelasticity theory is employed to study the distribution of temperature, deformation and stresses in an infinitely extended isotropic elastic thin plate containing a circular hole by taking (i) step-input of temperature and zero stress and (ii) step-input of stress and zero temperature change at the boundary of the hole. Because of the short duration of the second sound effects, short-time approximations of the solutions are studied using Laplace transform on time. It is found that the temperature, displacement and stresses are discontinuous at the wave fronts in case (i) and the exact discontinuities at the wave fronts are studied whereas in case (ii) temperature and displacement are found to be continuous at both the wave fronts but the stresses are found to be discontinuous at both the wave fronts.