Thermoelastic Materials Research Articles

Quasi-adiabatic approximation for thermoelastic surface waves in orthorhombic solids

An asymptotic model for time-harmonic motion in fully-coupled linear thermoelastic orthorhombic materials is presented. The asymptotic approach takes advantage of the observation that the parameter expressing departure from the purely adiabatic regime is extremely small in practice. Consequently, the leading order bulk response turns out to be non-dissipative, and is governed by the usual equations of elastodynamics with adiabatic material constants. In the case of isothermal stress-free boundary conditions, it is shown that thermoelastic interaction is dominated by a thermoelastic boundary layer. Hence, effective boundary conditions may be constructed, which duly account for the influence of this boundary layer and successfully describe dispersion and dissipation of surface waves to leading order. As an illustration, in the special case of an isotropic half-space with free isothermal boundary conditions, we recover the asymptotic results by Chadwick and Windle (1964). Numerical comparison of the dispersion curves for surface waves in an orthorhombic half-space shows excellent agreement between the exact fully-coupled thermoelastic problem and the corresponding quasi-adiabatic approximation, even for relatively large wavenumbers.

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.

Relaxation effects on thermoelastic interactions for time-dependent moving heat source under a recent model of thermoelasticity

In the present article, we investigate the thermal and elastic behaviour of an infinite thermoelastic material with a cylindrical cavity caused by a time-dependent moving heat source. The cavity surface is assumed to be subjected to a thermal shock. The formulation of the problem is applied for the recently proposed generalized thermoelastic model [Modified Green–Lindsay (MGL)] that takes into account the strain and temperature rates in the constitutive relations. We derive the governing equations in the present context along with the other two models, namely Lord–Shulman model and Green–Lindsay, by unifying governing equations under all these three models. The solutions are obtained for all three models in the Laplace transform domain, which are represented by unified expressions. The numerical computations for temperature, displacement and thermal stresses are carried out and depicted graphically. A detailed comparison is made amongst the results predicted by three models to highlight the effects of velocity of heat source and strain, temperature rate terms involved in the MGL model.

Investigation of thermo-elastic characteristics in functionally graded rotating disk using finite element method

Abstract In this research paper, displacement, stresses and strains are presented for rotating FGM disk with variable thickness by using finite element method (FEM). Thermo-elastic material properties and thickness of FGM disk continuously vary as exponential and power law function in radial direction along radius of disk. The value of Poisson's ratio is taken as constant. The problem of thermo-elasticity is converted into second order governing differential equation in terms of radial coordinate. This conversion is based upon equilibrium equation for disk and stress-strain relationship. The influence of variable thickness, angular velocity and functionally graded materials is discussed on thermo-elastic characteristics of rotating disk for exponential variation of material properties. Further, these thermo-elastic characteristics of disk are plotted for various values of non-homogeneity parameter under power law distribution of material properties. Thus, the investigations done in this research paper may be useful for industrial area in construction an appropriate FGM disk by controlling above mentioned parameters.

Influence of gravity, magnetic field, and thermal shock on mechanically loaded rotating FGDPTM structure under Green-Naghdi theory

This article deals with the theoretical investigation of deformations in a rotating isotropic functionally graded double porous thermoelastic material (FGDPTM) with voids by means of two temperature Green-Naghdi III (G-N III) model of generalized thermoelasticity. A gravitating magneto-double-poro-thermoelastic two-dimensional substrate is influenced by both thermal shock and inclined mechanical load at the free surface. The normal mode technique is carried out to derive the expressions for displacements, temperatures, volume fractions, and stresses. Numerical values for copper-like material are utilized to execute several graphical implementations representing the variations in the aforementioned variables in the presence and absence of different parameters. Furthermore, comparative studies among FGDPTM, functionally graded porous thermoelastic material (FGPTM), and functionally graded thermoelastic material (FGTM) structures are displayed graphically with and without two temperatures.

An efficient multi-scale computation of the macroscopic coefficient of thermal expansion: Application to the Resin Transfer Molding manufactured 3D woven composites

This paper presents a simple and computationally efficient multi-scale procedure to predict the macroscopic temperature dependent coefficient of thermal expansion (CTE) of any linearly thermoelastic material from isothermal mechanical simulations only. The approach relies on Levin’s demonstration that, in analytical homogenization, the effective coefficient of thermal expansion is related to the local coefficient of thermal expansion and the stress concentration tensor. For demonstration purposes, this procedure was applied to a 3D woven composite material. The proposed approach was successfully validated with full thermal simulations.

A General Study of Fundamental Solutions in Aniotropicthermoelastic Media with Mass Diffusion and Voids

The present paper deals with the study of a fundamental solution in transversely isotropic thermoelastic media with mass diffusion and voids. For this purpose, a two-dimensional general solution in transversely isotropic thermoelastic media with mass diffusion and voids is derived first. On the basis of the obtained general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic thermoelastic material with mass diffusion and voids is derived by nine newly introduced harmonic functions. The components of displacement, stress, temperature distribution, mass concentration and voids are expressed in terms of elementary functions and are convenient to use. From the present investigation, some special cases of interest are also deduced and compared with the previous results obtained, which prove the correctness of the present result.

Thermally induced vibrations in an inhomogeneous fiber-reinforced thermoelastic medium with gravity

PurposeThe present investigation is concerned with the two-dimensional deformations in an inhomogeneous fiber-reinforced thermoelastic medium under the influence of gravity in the context of Green–Lindsay theory.Design/methodology/approachMaterial properties are supposed to be graded in x-direction, and normal mode technique is adopted to obtain the exact expressions for the temperature field, displacement components and stresses.FindingsNumerical computations have been carried out with the help of MATLAB software, and the results are depicted graphically to observe the disturbances induced in the considered medium. Comparisons made within the theory of the physical quantities are shown in figures to highlight the effects of fiber reinforcement, inhomogeneity parameter, gravity and time.Originality/valueIn the present work, we have investigated the effects of fiber reinforcement, inhomogeneity parameter, gravity and time in an inhomogeneous, fiber-reinforced thermoelastic medium under the influence of gravity. Although various investigations do exist to observe the disturbances in a thermoelastic medium under the effects of different parameters, the work in its present form i.e. thermally induced vibrations in an inhomogeneous fiber-reinforced thermoelastic material with gravity has not been studied till now. The present work is useful and valuable for analysis of problems involving thermal shock, gravity parameter, fiber reinforcement, inhomogeneous and elastic deformation.

Peridynamic unit cell for effective properties of complex microstructures with and without defects

This study demonstrates the applicability of peridynamic unit cell (PD-UC) for predicting effective thermoelastic material properties of complex microstructures, and reduction in moduli due to the presence of defects. The comparisons for six different microstructures (i.e. Hexagonal pack, three-phase interphase, 0/90, spherical inclusions, woven-fiber, and random short-fiber) show remarkable agreement with the results from established models in the absence of defects. Unlike the existing models, the PD-UC is also capable of predicting the reduction in the presence of complex heterogeneity and defects. There exists no limitation on the number of constituent materials, and defects are introduced by simply breaking the PD bonds. Also, it permits orthotropic constituent materials. The PD-UC automatically permits the periodic boundary conditions without any constraint conditions.

Van Der Waals Force Mediated, Rotationally Aligned Dry-Transfer-Stacking of Two-Dimensional Tungsten Diselenide

Rotationally aligned, two-dimensional (2D), transition-metal dichalcogenides (TMDs) exhibit unique electronic, optical, and optoelectronic properties compared to random stacking. Rotationally aligned graphene stacking was demonstrated previously for numerous exotic phenomena, such as superconductivity, resonant tunneling, and moire pattern. However, rotationally aligned drytransfer techniques of TMDs, have yet to be demonstrated. Here, we show a simple method of selective cutting of a few-layer tungsten diselenide (WSe2) flake and rotationally aligning it by using dry-transfer stacking. The dry transfer techniques used for this study were adapted to maintain low sample contamination, a high-quality interface, a low number of defects. A combination of viscoelastic and thermoelastic materials was used for the TMD pickup and release to facilitate the rotationally aligned stacking. Aligned WSe2 stacks were characterized by Raman and photoluminescence spectroscopy to evaluate the integrity of the fabricated stack. This study highlights the possibility of using a rotationally aligned, artificial stacking method for exfoliated TMD materials for future electronic and optoelectronic applications.

A domain of influence theorem for a natural stress–heat-flux problem in the Moore–Gibson–Thompson thermoelasticity theory

The present paper is focused on the Moore–Gibson–Thompson (MGT) thermoelasticity theory. The MGT thermoelasticity theory is a generalized form of the Lord–Shulman (LS) thermoelasticity theory as well as the Green-Naghdi thermoelasticity theory with energy dissipation (GN-III). The present work is aimed at establishing the domain of influence results in the context of this new thermoelasticity theory. We consider a mixed boundary-initial value problem representing natural stress–heat-flux disturbance inside an isotropic and homogeneous medium. We establish an identity regarding this present problem. Further, we derive the domain of influence theorem based on this identity under the MGT thermoelasticity theory. From this theorem, we conclude that for prescribed bounded support of thermomechanical loading and for a finite time, the disturbance generated by the pair of stress and heat flux vanishes outside a bounded domain. It is also analyzed that the domain of influence relies on the thermoelastic material parameters. We further compare the present domain of influence results with the corresponding results of LS thermoelasticity theory.

Remarks on exponential stability for a coupled system of elasticity and thermoelasticity with second sound

We study the large time behavior of solutions to a linear transmission problem in one space dimension. The problem at hand models a thermoelastic material with second sound confined by a purely elastic one. We shall characterize all equilibrium states of the considered system and prove that every solution approaches one designated equilibrium state with an exponential rate as time goes to infinity. Hereto, we apply methods from the theory of strongly continuous semigroups. In particular, we obtain uniform resolvent bounds for the underlying generator. This removes the largeness assumption of elastic wave speeds imposed in [Y.P. Meng and Y.G. Wang, Anal. Appl. (Singap.) 13 (2015)] for having an exponential energy decay rate when the problem only has the trivial equilibrium. In an appendix we provide a similar exponential stability result for the case where heat conduction is modeled using Fourier's law.

Response of ramp-type heating in a monoclinic generalized thermoelastic material

PurposeThe two-dimensional deformation of a homogeneous, thermally conducting, monoclinic material has been studied by using Laplace and Fourier transforms technique. A linear temperature ramping function is used to more realistically model: thermal loading of the half-space surface. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating and loading. The displacements, stresses and temperature distribution so obtained in the physical domain are computed numerically and illustrated graphically. The comparison for Lord-Shulman (L-S), Green and Lindsay (G–L), Green and Naghdi (G–N) and Chandrasekharaiah and Tzou (CTU) theories have been shown graphically to estimate the effect of ramping parameter of heating for an insulated and temperature gradient boundaries.Design/methodology/approachThe design of the study is eigenvalue approachFindingsHomogeneous, thermally conducting monoclinic material has been taken under consideration to study the effect of linear temperature ramping parameter on temperature and normal displacement field. It is observed that magnitude of field quantities is large near the point of application of source for the non-dimensional values of time in all the four models. The numerical values for the field quantities are computed graphically for a wide range of values of finite pulse rise-time in the two situations t0 < t, t0 > t for generalized thermoelasticity theories.Originality/value(1) Governing equations for homogeneous, t0 thermally conducting, monoclinic material are described and solved. (2) Eigen value approach is used to solve the problem. (3) The effect of ramping parameter of heating has been studied for various models of the thermoelasticity to show the comparision between them.

Analysis of free vibrations in transradially isotropic spherically symmetric thermoelastic spheres

PurposeThe purpose of this manuscript is to study the vibration characteristics of the spherically symmetric solid and hollow spheres poised of a homogeneous thermoelastic material, based on the three dimensional coupled thermoelasticity.Design/methodology/approachIn this paper, matrix Fröbenius series solution is used to derive the frequency equations, for the field functions. Results have been applied on rigidly fixed boundary conditions.FindingsThe main finding of this paper is that the frequency of vibration of spherically symmetric sphere (structure is independent of theta and phi) increases with the increase of radius, for solid spheres and for hollow spheres with thickness to mean radius ratio. Deformation in the given materials increases with thickness to mean radius ratio of the hollow sphere.Originality/valueA numerical simulation has been done with the help of functional iteration method for solid and hollow thermoelastic spheres made of zinc and poly methyl meth acrylate materials for different boundary conditions. The computer simulated results in contempt of frequency, damping of vibration modes and displacement have been obtained graphically and compared with the existed results.

Electromagnetic, thermal and diffusive wave analysis on a two-temperature generalized thermo-elastic problem in a semi-infinite solid with cylindrical cavity subject to thermal loads

Our present work is concerned with the study of a semi-infinitely long, conducting solid with a cavity in cylindrical form in the context of magneto-thermo-elastic diffusion with two-temperature and three-phase-lag effect. The medium we have considered here is supposed to be initially quiescent. The material is assumed to be made of an isotropic homogeneous thermo-elastic material and put in a magnetic field which is uniform and acted in the direction of the axis of the cylindrical cavity. The solution to the problem is done in Laplace transform domain. Inversion process is applied to obtain the solution in space time domain and finally illustrated graphically.

Eucommia ulmoides gum-based engineering materials: fascinating platforms for advanced applications

Eucommia ulmoides gum (EUG) exhibits good rubber–plastic duality and great application potential in biomedicine, textiles, aerospace, and other fields. The extraction methods of EUG include mechanical (high-temperature cooking), alkali extraction, solvent, microbial (enzymatic hydrolysis), and comprehensive methods. However, the complicated preparation process and high cost of EUG greatly limit its application. EUG is composed mainly of trans-isoprene, and the high crystallinity of EUG at room temperature showing rigid plastics is due to the relatively regular and short identity period of its molecular chain. Through regulating the ratio of the three-phase structure of EUG (regular crystal region, completely irregular amorphous region, and intermediate region of transition pattern between the crystallized and amorphous regions), it exhibits rubber elasticity at room temperature. The application of EUG is closely related to its crystallinity and cross-linking degree. The double-bond modification of EUG by physical or chemical method can regulate its crystalline structure and cross-linking structure, so that EUG engineering materials that meet the performance requirements of multiple fields can be obtained. EUG with zero cross-linking degree is linear thermoplastic material, which is usually used in artificial limb, medical composite scaffold, composites denture soft lining, and modified plastic. EUG with low cross-linking degree is thermoelastic material, which is frequently used in the preparation of shape memory material, interfacial compatibilizer, and composite film. EUG with critical cross-linking degree is rubber-type material, which is regularly used in elastomer, self-healing material, and modified rubber. In this article, the extraction technology of EUG and its pros and cons and the structure and properties of EUG and their corresponding material states in the past 10 years were systematically discussed. The research progress of engineering materials in different states was introduced, and the effect of modification on the structure and properties of EUG was discussed. The future development direction of the materials was prospected.

Dynamic response of thermoelastic materials with voids subjected to ramp-type heating under three-phase-lag thermoelasticity

Porous materials have been widely used in aerospace, electronic communication, petrochemical and bio-medicine, etc. due to their attractive attributes such as low relative density, thermal and acoustical insulation and good permeability. For porous materials suffering high temperature gradient or ultrafast heating, etc., it is crucial to reveal the behaviors of the thermal-induced stress and deformation within them for guiding their potential applications and optimizations. In present work, the thermoelastic dynamic behaviors of a porous half-space subjected to a ramp-type heating is investigated based on the theory for thermoelastic porous materials and the three-phase-lag heat conduction model. The governing equations of the problem are formulated, and then, solved by using Laplace transform and its numerical inversion. The distributions of the nondimensional temperature, displacement, stress and volume fraction within the half-space are obtained and illustrated graphically. In calculation, the effects of time, ramp-heating time factor and thermal time-delay factors on the considered physical quantities are examined and discussed in detail. Comparisons of the variations of the considered quantities under three different theories are carried out and presented.

A domain of influence theorem under MGT thermoelasticity theory

The purpose of this article is to discuss domain of influence results under the Moore–Gibson–Thompson (MGT) thermoelasticity theory. We employ a mixed initial–boundary value problem concerning a homogeneous and isotropic material in view of the MGT thermoelasticity theory and establish the domain of influence theorem for potential–temperature disturbance. This theorem implies that the coupling of potential and temperature generates a thermoelastic disturbance, which vanishes outside the bounded domain for a prescribed bounded support of thermomechanical loading and for a finite time. The resulted bounded domain is subjected to the support of the prescribed load. The finite propagation of thermoelastic disturbance is also analyzed under the MGT theory, where the propagation speed depends on the parameters of the thermoelastic material. It is further shown that the domain of influence result for the present context reduces to the domain of influence result derived in the generalized thermoelasticity theory of Lord and Shulman under some conditions.

Exponential stability in Mindlin's Form II gradient thermoelasticity with microtemperatures of type III.

In this paper, we derive a nonlinear strain gradient theory of thermoelastic materials with microtemperatures taking into account micro-inertia effects as well. The elastic behaviour is assumed to be consistent with Mindlin's Form II gradient elasticity theory, while the thermal behaviour is based on the entropy balance of type III postulated by Green and Naghdi for both temperature and microtemperatures. The work is motivated by increasing use of materials having microstructure at both mechanical and thermal levels. The equations of the linear theory are also obtained. Then, we use the semigroup theory to prove the well-posedness of the obtained problem. Because of the coupling between high-order derivatives and microtemperatures, the obtained equations do not have exponential decay. A frictional damping for the elastic component, whose form depends on the micro-inertia, is shown to lead to exponential stability for the type III model.

Clustering-based multiscale topology optimization of thermo-elastic lattice structures

A multiscale clustering-based topology optimization for thermo-elastic lattice structures is studied based on the extended multiscale finite element method (EMsFEM). The strain energy of thermo-elastic lattice structures is chosen as the objective function. The microstructural configuration and the macrostructural distribution of the thermo-elastic lattice material are designed through topology optimization concurrently. The K-means clustering-based method is proposed to group the microstructures of the lattice materials. The effects of the number of clusters (groups), magnitude of the thermal loads, size factor of the microstructure, and material volume fraction on the optimization results are discussed. The results show that the clustering-based multiscale design optimization is superior to the classical multiscale design optimization of lattice structures.