Theory Of Thermoelasticity Research Articles

Efficient data-driven solution to thermoelastic mixed shock behavior of composite plates by considering the effect of agglomeration

This study presents an innovative path through the method of deep learning to inspect the mixed shock response of a latitudinally-graded agglomerated carbon-nanotubes enriched composite (LaG-ACNTEC) rectangular plate. The case study of this research is simultaneously exposed to thermomechanical and heat flux wave shocks at its edge expanded through the latitudinal direction. Equations of motion for this model are established on the bases of the linear thermoelasticity theory. Differential quadrature technique (DQT) is utilized for solving spatial dependency of these equations, while the Laplace transform and its inverse are utilized to solve temporal dependency of the system’s equations. Authors of this study reveal a novel path for increasing the computation efficiency of the approach by mounting a deep-learning-based method on the results determined by DQT and Laplace transform at designated points due to dynamic nature of the problem. Verification of the applied solution is performed based on a comparative study with the results of the published surveys. This study gives precious insights to designers for inspecting the mixed shock response of the composite structures by considering the effect of agglomeration and utilizing data-driven methods serving as accelerator of conventional solvers.

Effect of Magnetic Field and Inclined Load on a Two-Dimensional Thermoelastic Medium Under Gravity

This work aims to investigate the effects of magnetic field and inclined load on a two-dimensional thermoelastic medium under gravitational field. The problem is formulated in the context of refined dual-phase-lag Green–Naghdi (DPL GN) model. The bounding plane surface is heated by a non-Gaussian laser beam. The inclined load is supposed to be a linear combination of a normal load and a tangential load. Analytical formulas for several physical quantities are generated on the transformed domain using the Laplace and Fourier transform techniques. The inversion of double transform has been done numerically by using MATHEMTICA 10. The numerical inversion of Laplace transform is done by using the Zakian method (Halsted and Brown [Zakians technique for inverting Laplace transforms, J. Chem. Eng. 3 (1972) 312–313]). All physical quantities have been graphically depicted for the dual-phase-lag Green–Naghdi type III model (DPL GN-III), simple Green–Naghdi type III model (simple GN-III), Lord–Shulman model (LS) and classical thermoelasticity theory (CTE) to indicate the effect of magnetic field and the angle of inclination of the medium.

Photothermal interactions in a semiconducting fiber‐reinforced elastic medium with temperature‐dependent properties under dual‐phase‐lag model

AbstractThis article highlights the study of photothermoelastic interactions in a semiconducting fiber‐reinforced anisotropic medium with temperature‐dependent properties. The model is studied in the context of the photothermal transport process with dual‐phase‐lag theory of generalized thermoelasticity. The governing equations describe the interactions between elastic and plasma thermal waves. The normal mode analysis is employed to procure the exact expressions of the physical fields under investigation. A mechanical load is applied at the outer free surface of the medium to obtain the complete solution of the displacements, stresses, temperature, and carrier density distributions. Numerical results are obtained and displayed graphically with the help of MATLAB software. Some special cases of interest have been deduced from the present study and comparisons are also made among the different theories of thermoelasticity.

Mathematical significance of strain rate and temperature rate on heat conduction in thermoelastic material due to line heat source

The primary purpose of the present article is to investigate the effect of strain rate and temperature rate factors on a homogeneous, unbounded isotropic elastic medium originating due to continuous line heat source. This study is based on the modified Green-Lindsay Model (MGL) theory proposed by Yu et al. (2018). This model eliminates the discontinuous nature of the displacement field reported under the temperature-rate-dependent thermoelasticity theory (GL) established by Green and Lindsay. The present work obtains the analytical solution for the distributions of stress components, temperature and displacement through the potential function approach accompanied by the Laplace transform method. The inverse Laplace transformation is performed by using short-time approximation method to find the approximated analytical solution of the problem in space-time domain. A detailed analysis of solution is discussed for MGL model and compared to the results predicted by other existing generalized thermoelastic models. The effect of strain-rate and temperature-rate-terms is acknowledged explicitly in mathematical formulation and other significant effects are notified. However, this new model predicts the infinite speed of disturbance analogous to classical theory.

Nonlocal dual-phase-lag thermoelastic damping in small-sized circular cross-sectional ring resonators

The purpose of current research is to establish a theoretical size-dependent framework for estimating the amount of thermoelastic damping (TED) in miniaturized rings with circular cross section via the nonlocal dual-phase-lag (NDPL) generalized thermoelasticity theory, as one of the most exhaustive non-Fourier heat conduction models. The method used to achieve this goal is based on the definition of TED in the energy dissipation (ED) approach. To do so, after deriving heat equation in the context of NDPL model, the distribution of temperature all over the volume of the ring is specified. Then, the relations of dissipated thermal energy and strain energy in the ring are obtained. Lastly, by employing ED approach, a formula comprising the nonclassical parameters of NDPL model is rendered to determine TED value in small-scaled toroidal rings. By presenting various numerical examples, the dependence of TED on influential parameters including nonclassical thermal constants in NDPL model, ring geometry, vibrational mode number and ring material is surveyed. The Findings enlighten that the inclusion of nonlocal parameter into the model can have conspicuous impacts on TED value, especially in smaller rings or higher vibrational mode numbers. The results also reveal that among the investigated materials (i.e. silicon, copper, silver, and lead), rings made of lead and silicon exhibit the maximum and minimum TED values, respectively.

Heat flow influence on the Cauchy stress tensor in a thermal wave

Rational thermodynamics with relaxing heat fluxes is used in this work to obtain the constitutive equations of thermoelasticity. It is found that it is possible to formulate the governing equations of the medium where the density of internal energy per unit mass depends on the heat flux, while the density of entropy per unit mass may not depend on it. A situation where the density of the entropy per unit mass depends on the heat flux, while the density of internal energy per unit mass does not, is also possible. A model of a thermoelastic material with a relaxing heat flux, where the characteristic relaxation time of the heat flux is a constant of the material, is considered in detail in this paper. It is shown that the Cauchy stress tensor in this model is not only a function of the temperature and deformations of the medium, but also depends on the heat flux. This gives rise to new effects not present in the classical theory of thermoelasticity. The specific heat of the material will also depend on the magnitude of the heat flux.The paper considers the application of the theory to the modelling of thermal processes during ion plasma treatment of a polymeric material.

An improved theory of thermoelasticity for ultrafast heating of materials using short and ultrashort laser pulses

This paper introduces an improved thermoelastic theory designed specifically to address the challenges posed by fast and ultrafast heating of materials. The proposed theory incorporates a time delay in the temperature gradient and introduces the rate of temperature gradient as an additional term in the heat equation. This term accounts for the phase lag and the precedence of the temperature gradient and heat flux vector. By leveraging the sign of the temperature gradient rate, the theory automatically determines the precedence of either the temperature gradient or the heat flux vector. To verify the effectiveness of the proposed theory, experiments reported in the literature were simulated using several theories, namely the classical, Lord-Schulman (LS), Green-Lindsay (GL), dual-phase-lag (DPL), and the presented theory. The simulations considered the effects of relaxation times and pulse duration on the results. The findings reveal that for pulse durations shorter than 50 ps, the second-order time derivative of the temperature gradient becomes a crucial term in the energy equation for accurately predicting temperature profiles. Additionally, as the pulse duration decreases, the sensitivity to relaxation times increases. Regarding the surface temperature corresponding to the material ablation threshold, it is observed that for an 80 fs laser pulse, the ablation temperature falls between the boiling and critical temperatures, significantly higher than the boiling temperature associated with the ablation by a 270 ps pulse duration. Lastly, the simulation results exhibit a high level of agreement with the experimental data, particularly in terms of displacements, further validating the accuracy of the presented simulations.

Nonlocal fiber-reinforced double porous material structure under fractional-order heat and mass transfer

PurposeThe purpose of this study is to analyze the thermo-diffusion process in a semi-infinite nonlocal fiber-reinforced double porous thermoelastic diffusive material with voids (FRDPTDMWV) in light of the fractional-order Lord–Shulman thermo-elasto-diffusion (LSTED) model. By virtue of Eringen’s nonlocal elasticity theory, the governing equations for the considered material are developed. The free surface of the substrate is governed by the inclined mechanical load and thermal and chemical shocks.Design/methodology/approachWith the aid of the normal mode technique, the solutions of the nondimensional coupled governing equations have been obtained.FindingsThe expressions of field variables are obtained analytically. By using MATHEMATICA software, various graphical implementations are presented to describe the impacts of angle of inclination, fractional-order and nonlocality parameters. The present model is also validated on the basis of some comparative studies with some preestablished cases.Originality/valueAs observed from the literature survey, many different studies have been carried out by taking into account the deformation analysis in nonlocal double porous thermoelastic material structures and thermo-mechanical interaction in fiber-reinforced medium under fractional-order thermoelasticity theories. However, to the best of the authors’ knowledge, no research emphasizing the thermo-elasto-diffusive interactions in a nonlocal FRDPTDMWV has been carried out. Moreover, the effect of fractional-order LSTED theory on fiber-reinforced thermoelastic diffusive half-space with double porosity has not been illuminated till now, which significantly defines the novelty of the conducted research.

On the supersonic vibrations of the advanced composite quasi-3D hyperbolic refined high-order sector annular/circular structure in thermal environment

Functionally graded materials (FGMs) have been used in many high-tech engineering fields because they could improve material properties. Some well-known applications of these materials are over different geometrical shapes like shells and plates. Multi-directional FGMs have the main role in the improvement of multi-functional materials by introducing modern materials. A detailed study of sector annular/circular disks with different thickness directions has been carried out. In practice, the material properties need to be categorized in other directions as well. Sector annular/circular disks made of multi-dimensional FGM (MD-FGM) are vulnerable to high-temperature gradients and enormous deflections. Using the discrete singular convolution method (DSCM), we investigated asymmetric deformations of MD-FG sector annular/circular disk tolerating thermo-aerodynamics loads. What makes this research unique is using thickness classification for the material properties of the disk while radial and circumferential directions follow an exponential trend. In practical conditions, this assumption would result in a more accurate simulation. Having developed equations based on quasi-3D new refined theory (Q3D-NRT) considering the effect of thickness stretching, we solved the equations based on our conditions. With the aid of COMSOL multi-physics finite element simulation, the results are verified and new recommendations for improving the stability of presented MD-FG sector disks are reported. This research might be helpful for scientists working in the field of thermoelastic theory of disks. Since it is very important to have small and uniform thermal stresses in every direction of the materials, the study’s results could be used as a trustworthy database to determine a material property function.

Investigation on the thermoelastic response of a porous microplate in a modified fractional-order heat conduction model incorporating the nonlocal effect

In recent years, the application of porous materials in practical engineering has become increasingly common. Under extreme thermal conditions, how to accurately describe the heat conduction and structural response of porous materials is a key issue in the structural safety and functional design of porous materials. Among them, it is particularly important to consider the size-dependent and memory-dependent effects for small-sized structures or microdevices of porous materials. To address these issues of porous structures and to guide their applications as well as optimization, this paper first investigates the thermoelastic transient response of porous microplates subjected to thermal and stress shocks at the left boundary based on the Atangana-Baleanu (AB) fractional-order generalized thermoelastic theory by considering nonlocal effects and fractional-order strain, which is combined with the thermoelasticity theory of porous materials and the dual-phase-lag (DPL) heat conduction model. The governing equations are then established and solved using the Laplace transform and its numerical inversion. Finally, the effects of newly defined fractional order parameters, nonlocal parameters and the initial magnitude of the mechanical shock on the dimensionless temperature, volume fraction field, displacement and stress distribution are discussed and displayed graphically.

On the coupled linear theory of thermoelasticity for nanomaterials which triple porosity

In this paper, the linear mathematical model of thermoelastic nanomaterials with triple porosity is proposed in which the coupled phenomenon of Darcy’s law and the concept of the volume fractions of three levels of pores (macro-, meso- and micropores) is considered. Then, the 3D internal and external basic boundary value problems (BVPs) of steady vibrations of this model are formulated. The radiation conditions are established and Green’s identities are obtained in the considered theory. Finally, the uniqueness theorems for classical solutions of the above mentioned BVPs are proved.

A novel approach to optimize material distributions of rotating functionally graded circular disk under minimum and prescribed stresses

This study focuses on the optimization of a rotating disk composed of functionally graded material (FGM), which is subjected to both inertial and thermal loads. The novelty of this study lies in the fact that the optimum material distribution for achieving minimum and prescribed stress profiles in the FGM disk is not limited to the priori assumed functional variation, unlike the case in the majority of existing literature. An optimization model is developed to solve the inverse problem and obtain the volume fraction or material distribution of the FGM disk corresponding to the minimum and prescribed stress profiles. First, the problem is formulated utilizing second-order differential equations in accordance with theories of two-dimensional thermoelasticity. Then, the second-order governing differential equation, with the design variables being the volume fractions across the disk, is used in an objective function. Finally, the determination of the global minimum value of the objective function is achieved by the differential evolution method through the utilization of a standard finite element approach for solving the differential equation. Thus, the volume fraction distribution of the disk corresponding to the objective function is obtained. The present investigation pertains to two distinct forms of the objective function, specifically, an objective function for minimum stress and another for prescribed stress. In addition, a mathematical model of the direct problem is developed to analyze the minimum stress profile of the FGM disk, with the optimum material distribution derived from the optimization model provided as input. The models are validated through a comparison of their results with those found in existing literature. The numerical results of this study ensure that it is feasible to design an FGM disk with optimum material distribution, achieving the minimum and prescribed stress profile within the disk. It is also revealed that the optimum material distribution is significantly influenced by the stress profile, temperature field, angular speed, and radial thickness of the disk.

Thermo-hydro-mechanical nonlocal response on porous deep-sea sediments under vibration of mining vehicle

The excessive deformation of deep-sea sediments caused by the vibration of the mining machine will adversely affect the efficiency and safety of mining. This paper reports the study of coupled thermo-hydro-mechanical problem for saturated porous deep-sea sediments, subjected to the vibration of the mining vehicle. Based on nonlocal Moore–Gibson–Thompson thermoelastic theory and Darcy’s law, the model for thermo-hydro-mechanical dynamic response for saturated porous deep-sea sediments under the vibration of mining vehicle is established. Analytical solutions for vertical displacement, excess pore water pressure, vertical stress, temperature and the change in the volume fraction field have been obtained on implementing the normal mode analysis, and the numerical results have been depicted graphically. The result provides the direction on how the vibration frequency and the loading amplitude can affect the physical quantities of the foundation of the seabed. The influence of nonlocality and memory effect on the seabed is also reported.

WHY ARE EPOXY-COATED STEEL REBARS PROHIBITED IN BRIDGE STRUCTURES IN SOME REGIONS?

One of the common ways in many countries to protect steel reinforcement from corrosion in reinforced concrete structures is to cover its surface with a thin layer of epoxy resin. However, in practice, in many cases, the anti-corrosion effect of epoxy coating was not significant, and the durability of reinforced con-crete bridge structures was lower than those where steel reinforcement was not coated with epoxy resin. Ex-perts believe that one of the factors that affects the corrosion resistance of steel reinforcement with epoxy coat-ing in reinforced concrete is the presence of mechanical damage in the epoxy coating of the reinforcing rod, through which moisture can penetrate. Therefore, in some countries, instructions have been developed for the prevention of such damage at the stages of applying an epoxy coating to the armature, its storage, transporta-tion, and construction and assembly work in the manufacture of reinforced concrete structures. This article discusses the thermomechanical mechanism of violation of the internal structural integrity of concrete rein-forced with steel rods with an epoxy coating, which is caused by a high value of its coefficient of linear thermal expansion and the epoxy coating itself. Using the methods of the theory of thermoelasticity, a mathematical model of this phenomenon was developed, a system of solving differential equations was formed, and its solu-tion was constructed. It was established that even with relatively minor temperature changes in the concrete environment in the area of its contact with the reinforcement, cracks and damages occur along the entire length of the steel reinforcement. All this contributes to further destructive processes and reducing the durabil-ity of reinforced concrete bridge structures.

Surface waves in piezoelectric semiconductor by using Eigen value approach

The article is about the propagation of surface waves through electrically conducting medium. The piezoelectric medium is an n-type semiconductor. The finite deformation caused in the medium results in generation of elastic disturbance that propagate through the medium in the form of surface waves. According to the theory of thermoelasticity, temperature also propagate in the medium in the form of thermal waves. The heat propagation through the medium is encountered by classical heat conduction model derived from Fourier’s law of heat conduction. The analytical solution for system of governing equations is obtained by using Normal mode analysis method along with Eigen value approach. Secular equation containing the information of surface waves is obtained for some specific boundary conditions at the surface . Furthermore, the theoretical results obtained are represented graphically for a particular medium.

A peridynamic model based on generalized thermoelastic theory in a plate with oblique cracks

In this paper, a peridynamic model based on generalized thermoelastic theory is derived by irreversible thermodynamics. This model avoids the spatial derivative and can be easily applied to generalized thermoelastic problems with discontinuities. The transient temperature response is captured using the non-Fourier CattaneoVernotte (C-V) model. The interaction integral is employed to calculate the transient thermal stress intensity factors (TSIFs). Numerical examples are presented for analyzing the effects of crack orientation angle and multi-crack distribution on transient thermoelastic response. And the crack propagation behavior under non-Fourier thermal shock is further discussed in detail. It is found that with the increase of the angle between inner crack and heating boundary, the sensitivity of mode-I TSIFs to the non-Fourier effect increases, while the sensitivity of mode-II TSIFs to the non-Fourier effect decreases. This peridynamic model may be useful for understanding the crack behaviors of thermal protection materials under thermal shock.

Numerical analysis of the stressed-deformed state of a tubular element under thermal loading

In articles [2-5] solving relations and the block iteration method algorithm for solving linear and nonlinear equations by the semi-analytical finite element method for curvilinear heterogeneous prismatic bodies are implemented. In article [1], a numerical study of the convergence of the solution was performed, a wide range of test problems for bodies with smoothly and abruptly changing physical and geometric characteristics in elastic and elastic-plastic settings were considered. In [6], to confirm the reliability of the results obtained on the basis of the semi-analytical method of finite elements, the effectiveness of the application of this approach for the calculation of curvilinear inhomogeneous prismatic objects is shown. Solving control problems of the theory of elasticity, thermoelasticity, and thermoplasticity, as well as shape change problems, makes it possible to draw a conclusion about the reliability of the results of the research of a selected class of objects based on the developed methodology and implements its application program package.
 In this paper, using the methodology outlined in the above works, the results of the numerical solution of the problem, which have an applied value, were presented. The stress-strain state of a tubular element with a rectangular cutout under conditions of thermoforce loading was studied. As a rule, solving similar problems is carried out in a flat setting without taking into account the bending load. This approach greatly simplifies the formulation of the problem, but leads to very significant errors in the results. At zero value of the bending load, a good agreement of the planar and spatial solutions is observed. The presence of a bending load leads to deviation of the curves from their initial position. The maximum discrepancy of the results is almost 50%.
 The analysis of this structure from the standpoint of the spatial problem of thermoplasticity, which ensures taking into account the dependence of the physical and mechanical characteristics of the material on temperature and taking into account the bending load on the section of the cut, allowed us to reveal the real features of its deformation.

A Method for Analysis of Nonlinear Deformation, Buckling, and Vibrations of Thin Elastic Shells with Inhomogeneous Structures

The formulation of the problem and the method of analysis of the stress-strain state, buckling and vibrations of elastic shells with inhomogeneous structure are considered. The modal analysis of the shells is performed at each stage of loading. The method allows one to study the behavior of shells with a complex shape of the middle surface, geometric features throughout the thickness, and a multilayer material structure under thermomechanical loading. We approximate a thin shell with one finite element (FE) over the entire thickness. At the same time, we use spatial FEs of the same type to model shell portions with stepwise-varying thickness. So we apply the universal finite element. It is based on an isoparametric 3D element with polylinear shape functions for coordinates and displacements and has additional parameters. The universal finite element can be transformed (modified) to accurately describe portions of the shell with stepped-variable thickness. This element can be eccentrically displaced relative to the average surface of the shell and change its own thickness. The side edges of neighboring FEs are in continuous contact, and the FE allows simulating sharp bends of the shell. The approach is modern and easy to implement, since it is based on the use of the relations of the three-dimensional geometrically nonlinear theory of thermoelasticity and the application of the moment finite-element scheme. The effectiveness of the method is demonstrated on classical test examples. The convergence, accuracy and reliability of the obtained solutions are investigated. Comparison of the results of calculations obtained by the moment finite-element scheme with the data of other authors shows a good agreement between the solutions.

Influence of the fractional-order strain on an infinite material with a spherical cavity under Green-Naghdi hyperbolic two-temperature thermoelasticity theory

In this work, a novel mathematical model of thermoelastic, homogenous, isotropic, and infinite medium with a spherical cavity has been constructed. Under the hyperbolic two-temperature Green-Naghdi theory of thermoelasticity type-I and type-III with fractional-order strain, the governing equations have been established. The bounding surface of the cavity has been thermally loaded by a ramp-type heat and is connected to a rigid foundation which prevents volumetric strain. Different values of the fractional-order and two-temperature parameters have shown numerical results for the dynamical and conductive temperature increment, strain, displacement, and average of principal stresses, which are graphically applicable to all the functions studied. The fractional-order parameter has significant effects on stress and strain distributions, while it has a limited effect on the dynamical and conductive temperatures increment. The hyperbolic two-temperature parameter has significant effects on all studied functions based on Green-Naghdi models of type-1 and type-II. Moreover, the ramp-time heat parameter has a significant impact on all the studied functions under all the studied models of thermoelasticity.

Generalized thermoelasticity study in ultrashort pulsed laser machining of ceramic considering material removal and variable material properties

Ceramic materials are widely used in engineering due to their excellent properties, but they are difficult to be machined by conventional techniques. Ultrashort pulsed laser is an applicable tool to achieve high-quality processing of these hard-brittle materials. However, the ultrashort thermalization time and complex interactions in laser processing bring great difficulty to describe thermal-mechanical responses precisely. For this purpose, we establish a model for ceramics irradiated by femtosecond pulsed laser in the context of Green-Lindsay generalized thermoelastic theory, considering the effect of material removal and temperature-dependent material properties. Thermoelastic responses and the effect of laser parameters in the machining considering material removal are obtained by means of Finite Element Method. Results show that classical thermoelastic theory underestimates thermal stresses, while G-L thermoelastic theory predicts more accurate responses. Laser parameters, including laser intensity and pulse duration, significantly affect the thermoelastic responses and the process of material removal, which indicates the necessity of laser parameter optimization for reduced thermal stresses and higher processing efficiency. Temperature-dependence of material properties must be considered, as it has pronounced influences on thermoelastic responses. This study can be used as the preparation for the structural safety design in ultrashort pulsed laser machining.