A novel electron-phonon coupling thermoelasticity with Burgers electronic heat transfer

The electron-phonon interaction can reveal the microscopic mechanism of heat transfer in metals.The two-step heat conduction considering electron-phonon interaction has become an effective theoretical model for extreme environments,such as micro-scale and ultrafast processes.In this work,the two-step heat transfer model is further extended by considering the Burgers heat conduction model with the secondorder heat flux rate for electrons.Then,a novel generalized electron-phonon coupling thermoelasticity is proposed with the Burgers electronic heat transfer.Then,the problem of one-dimensional semi-infinite copper strip subject to a thermal shock at one side is studied by the Burgers two-step(BTS)model.The thermoelastic analytical solutions are systematically derived in the Laplace domain,and the numerical Laplace inversion method is adopted to obtain the transient responses.The new model is compared with the parabolic two-step(PTS)model and the hyperbolic two-step(HTS)model.The results show that in ultrafast heating,the BTS model has the same wave front jump as the HTS model.The present model has the faster wave speed,and predicts the bigger disturbed regions than the HTS model.More deeply,all two-step models also have the faster wave speeds than one-step models.This work may benefit the theoretical modeling of ultrafast heating of metals.

DEPENDENCE OF MODULUS OF ELASTICITY AND THERMAL CONDUCTIVITY ON REFERENCE TEMPERATURE IN GENERALIZED THERMOELASTICITY FOR AN INFINITE MATERIAL WITH A SPHERICAL CAVITY

The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The inner surface of the cavity was taken to be traction free and acted upon by a thermal shock to the surface. Laplace transforms techniques were used to obtain the solution by a direct approach.The inverse Laplace transforms was obtained numerically.The temperature,displacement and stress distributions are represented graphically.

MULTI-SCALE FE COMPUTATION FOR THE STRUCTURES OF COMPOSITE MATERIALS WITH SMALL PERIODIC CONFIGURATION UNDER CONDITION OF COUPLED THERMOELASTICITY

In this paper,the multi-scale computational method for a structure of composite materials with a small periodic configuration under the coupled thermoelasticity condition is presented. The two-scale asymptotic(TSA)expression of the displacement and the increment of temperature for composite materials with a small periodic configuration under the condition of thermoelasticity are briefly shown at first,then the multi-scale finite element algorithms based on TSA are discussed.Finally the numerical results evaluated by the multi-scale computational method are shown.It demonstrates that the basic configuration and the increment of temperature strongly influence the local strains and local stresses inside a basic cell.

The effect of fractional thermoelasticity on a two-dimensional problem of a mode I crack in a rotating fiber-reinforced thermoelastic medium

This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The fractional order theory of thermoelasticity is used to obtain the analytical solutions for displacement components, force stresses, and temperature. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The variations of the considered variables with the horizontal distance are illustrated graphically. Some particular cases are also discussed in the context of the problem. Effects of the fractional parameter, reinforcement, and rotation on the varia- tions of different field quantities inside the elastic medium are analyzed graphically. Comparisons are made between the results in the presence and those in the absence of fiber-reinforcing, rotating and fractional parameters.

Reflection of three-dimensional plane waves at the free surface of a rotating triclinic half-space under the context of generalized thermoelasticity

The reflection of three-dimensional(3D) plane waves in a highly anisotropic(triclinic) medium under the context of generalized thermoelasticity is studied. The thermoelastic nature of the 3D plane waves in an anisotropic medium is investigated in the perspective of the three-phase-lag(TPL), dual-phase-lag(DPL), Green-Naghdi-III(GNIII), Lord-Shulman(LS), and classical coupled(CL) theories. The reflection coefficients and energy ratios for all the reflected waves are obtained in a mathematical form. The rotational effects on the reflection characteristics of the 3D waves are discussed under the context of generalized thermoelasticity. Comparative analyses for the reflection coefficients of the waves among these generalized thermoelastic theories are performed. The energy ratios for each of the reflected waves establish the energy conservation law in the reflection phenomena of the plane waves. The highly anisotropic materials along with the rotation may have a significant role in the phenomenon of the reflection behavior of the 3D waves. Numerical computations are performed for the graphical representation of the study.

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.

Size-dependent thermoelasticity of a finite bi-layered nanoscale plate based on nonlocal dual-phase-lag heat conduction and Eringen's nonlocal elasticity

The size effects on heat conduction and elastic deformation are becoming significant along with the miniaturization of the device and wide application of ultrafast lasers.In this work,to better describe the transient responses of nanostructures,a size-dependent thermoelastic model is established based on nonlocal dual-phase-lag(N-DPL)heat conduction and Eringen's nonlocal elasticity,which is applied to the one-dimensional analysis of a finite bi-layered nanoscale plate under a sudden thermal shock.In the numerical part,a semi-analytical solution is obtained by using the Laplace transform method,upon which the effects of size-dependent characteristic lengths and material properties of each layer on the transient responses are discussed systematically.The results show that the introduction of the elastic nonlocal parameter of Medium 1 reduces the displacement and compressive stress,while the thermal nonlocal parameter of Medium 1 increases the deformation and compressive stress.These findings may be beneficial to the design of nano-sized and multi-layered devices.

DIFFERENTIAL-ALGEBRAIC APPROACH TO COUPLED PROBLEMS OF DYNAMIC THERMOELASTICITY

An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations （DAEs） where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula （BDF） using a fully implicit algorithm. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.

STUDY ON THE SOLUTION OF DYNAMIC THERMOELASTICITY SYSTEM

The problem of the coupled thermoelasticity has a W. A. Day has studied the nature of the solution ofthe system in which the constant b ￣ 0. In this paper,the existence,uniqueness and properly posed problem of the solution of the system in which the constant b 4 0 is studied.

Thermoelasticity of CaO from first principles

The thermoelastic properties of CaO over a wide range of pressure and temperature are studied using density functional theory in the generalized gradient approximation. The transition pressure taken from the enthalpy calculations is 66.7 GPa for CaO, which accords with the experimental result very well. The athermal elastic moduli of the two phases of CaO are calculated as a function of pressure up to 200 GPa. The calculated results are in excellent agreement with existing experimental data at ambient pressure and compared favourably with other pscudopotential predictions over the pressure regime studied. It is also found that the degree of the anisotropy rapidly decreases with pressure increasing in the B1 phase, whereas it strongly increases as the pressure increases in the B2 phase. The thermodynamic properties of the B1 phase of CaO are predicted using the quasi-harmonic Debye model; the heat capacity and entropy arc consistent with other previous results at zero pressure.

Effects of three-phase-lag on two-temperature generalized thermoelasticity for infinite medium with spherical cavity

The thermoelastic interaction for the three-phase-lag （TPL） heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory （2TT）. The heat conduction equation in the theory of TPL is a hyperbolic partial differential equation with a fourth-order derivative with respect to time. The medium is assumed to be initially quiescent. By the Laplace trans- formation, the fundamental equations are expressed in the form of a vector-matrix differ- ential equation, which is solved by a state-space approach. The general solution obtained is applied to a specific problem, when the boundary of the cavity is subjected to the ther- mal loading （the thermal shock and the ramp-type heating） and the mechanical loading. The inversion of the Laplace transform is carried out by the Fourier series expansion tech- niques. The numerical values of the physical quantity are computed for the copper like ma- terial. Significant dissimilarities between two models （the two-temperature Green-Naghdi theory with energy dissipation （2TGN-III） and two-temperature TPL model （2T3phase）） are shown graphically. The effects of two-temperature and ramping parameters are also studied.

State-space approach to two-temperature generalized thermoelasticity without energy dissipation of medium subjected to moving heat source

In this work, a model of two-temperature generalized thermoelasticity without energy dissipation for an elastic half-space with constant elastic parameters is constructed. The Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions. The general solutions are applied to a specific problem of a half-space subjected to a moving heat source with a constant velocity. The inverse Laplace transforms are computed numerically, and the comparisons are shown in figures to estimate the effects of the heat source velocity and the two-temperature parameter.

MAC Models in Thermoelasticity

There are two types of singularities in the linear thermoelasticity.The first one arises in the field of stresses if a force is applied to one point of the body.This singularity is physical and should be accepted.The second type of singularities is nonphysical and they arise in the fields of displacements and temperatures.There exist the nonlocal theories and gradient theories which have the goal to introduce the finite stresses instead of the infinite ones.The MAC model of the thermoelasticity is created to avoid the nonphysical singularities and it accepts the infinite stresses.MAC is the method of additional conditions,which allows introducing the new model to use the classical model,plus additional condition of the physical nonsingularity and/or condition of the good behavior of the solutions at infinity.The MAC Green′s functions for the heat conduction and for the elasticity could be introduced using the differential MAC models.The infinite and finite bodies are considered.The principle of superposition is applied to obtain the integral equations to solve the boundary value problems.The strength criteria based on finite stresses could be changed in this model because the infinite stresses are allowed.The strength criteria based on deformations are applicable.Classification of MAC models is given.

Potential Method in the Theory of Thermoelasticity with Microtemperatures for Microstretch Solids

The linear equilibrium theory of thermoelasticity with microtemperatures for microstretch solids is considered.The basic internal and external boundary value problems(BVPs)are formulated and uniqueness theorems are given.The single-layer and double-layer thermoelastic potentials are constructed and their basic properties are established.The integral representation of general solutions is obtained.The existence of regular solutions of the BVPs is proved by means of the potential method(boundary integral method)and the theory of singular integral equations.

Generalized Thermoelasticity Problem of Material Subjected to Thermal Loading Due to Laser Pulse

This work is devoted to a study of the induced temperature and stress fields in an elastic half space in context of clas-sical coupled thermoelasticity and generalized thermoelasticity in a unified system of equations. The half space is con-sidered to be made of an isotropic homogeneous thermoelastic material. The bounding plane surface is heated by a non-Gaussian laser beam with pulse duration of 2 ps. An exact solution of the problem is first obtained in Laplace transform space. Since the response is of more interest in the transient state, the inversion of Laplace transforms have been carried numerically. The derived expressions are computed numerically for copper and the results are presented in graphical form.

THERMOELASTICITY ANALYSIS OF FINITE COMPOSITE LAMINATES WEAKENED BY MULTIPLE ELLIPTICAL HOLES

A finite composite laminate weakened by multiple elliptical holes of arbitrarydistribution, arbitrary orientation and arbitrary dimension, is treated as an anisotropic,finite multiple connected thin plate. Using the complex potential method in planetheory of heat conduction and elastictiy of an anisotropic body, the analytical solutionof a finite composite laminated plate subjected io arbitrary mechanical and thermalloads with multiple elliptical holes is. obtained by means of the Faber series expansion,mapping and the least square boundary collocation technique. The effects of someparameters on the thermostress distribution are studied in detail. Some conclusions aredrawn.

Transient response of multilayered hollow cylinder using various theories of generalized thermoelasticity

The present paper deals with thermoelastic problems of finitely long hollow cylinder com-posed of two different materials with axial sym- metry. The medium is traction-free, with neglig-ible body forces and with internal and external heat generations. The governing equations for different theories of the generalized thermoe-lasticity are written in terms of displacement and temperature increment. The exact solution of the problem;using different theories of generalized thermoelasticity;has been deduced. The analytical expressions for displacements, temperature and stresses are found in final forms, and a numerical example has been taken to discuss the effect of the relaxation times. Finally, the results have been illustrated graphi- cally to find the responses of different theories.

Two-Temperature Generalized Thermoelasticity without Energy Dissipation of Infinite Medium with Spherical Cavity Thermally Excited by Time Exponentially Decaying Laser Pulse

This work is dealing with two-temperature generalized thermoelasticity without energy dissipation infinite medium with spherical cavity when the surface of this cavity is subjected to laser heating pulse. The closed form solutions for the two types of temperature, strain, and the stress distribution due to time exponentially decaying laser pulse are constructed. The Laplace transformation method is employed when deriving the governing equations. The inversion of Laplace transform will be obtained numerically by using the Riemann-sum approximation method. The results have been presented in figures to show the effect of the time exponentially decaying laser pulse and the two temperature parameter on all the studied fields.

Determination of a U-Notch Stress Concentration Factor Using Thermoelasticity

This paper uses the TSA （therrnoelastic stress analysis） technique to determine the stress concentration factor （Kt） of a U-notch in an aluminum plate, and then compares the results with those obtained from a FEA （finite elements analysis） of the same specimen. In order to do so, it devises a calculation procedure to extrapolate the thermoelastic data near the tip of the notch and then applies the resulting algorithm to seven distinct experiments that had different loading frequencies, mean loads and load ranges. The overall positive results suggest that the technique may be suitable for Kt measurements in real-world structures. A discussion about the calibration factor of the thermoelastic data is included by confronting the calibration results using independent tensile uniaxial tests and using the U-notch TSA and FEA paired specimen data.

Magneto-Thermoelasticity with Thermal Shock Considering Two Temperatures and LS Model

The present investigation is intended to demonstrate the magnetic field,relaxation time,hydrostatic initial stress,and two temperature on the thermal shock problem.The governing equations are formulated in the context of Lord-Shulman theory with the presence of bodily force,two temperatures,thermal shock,and hydrostatic initial stress.We obtained the exact solution using the normal mode technique with appropriate boundary conditions.The field quantities are calculated analytically and displayed graphically under thermal shock problem with effect of external parameters respect to space coordinates.The results obtained are agreeing with the previous results obtained by others when the new parameters vanish.The results indicate that the effect of magnetic field and initial stress on the conductor temperature,thermodynamic temperature,displacement and stress are quite pronounced.In order to illustrate and verify the analytical development,the numerical results of temperature,displacement and stress are carried out and computer simulated results are presented graphically.This study helpful in the development of piezoelectric devices.