Thermoelastic Behavior Research Articles

Physics-informed neural network solution for thermo-elastic cavity expansion problem

ABSTRACT This paper proposes a physics-informed neural network (PINN) to solve the thermo-elastic coupled cavity expansion problem under plane strain conditions. The solid is modelled as a linear thermo-elastic material, and cavity expansion is driven by a constant temperature and a radial displacement subjected to the inner cavity wall. Governing partial differential equations (PDEs) for the problem is firstly presented, and an analytical solution is available to help benchmark the PINN approach. Then, the PDEs are normalised into dimensionless forms and neural network details for solving the coupled PDEs are demonstrated. Finally, the performance of the PINN approach is shown by comparison with the analytical benchmark solution and it is found that the PINN can predict thermo-elastic cavity expansion behaviour with high accuracy. The PINN approach and the analytical solution can also serve as a benchmark for solving thermo-elastic coupled problems in geotechnical engineering by more advanced PINN.

Homogenization of Thermal Properties in Metaplates.

Three-dimensional metamaterials endowed with two-dimensional in-plane periodicity exhibit peculiar thermoelastic behaviour when heated or cooled. By proper design of the unit cell, the equivalent thermal expansion coefficient can be programmed and can also reach negative values. The heterogeneity in the third direction of such metamaterials also causes, in general, a thermal-induced deflection. The prediction of the equivalent thermal properties is important to design the metamaterial suitable for a specific application. Under the hypothesis of small thickness with respect to the global in-plane dimensions, we make use of asymptotic homogenization to describe the thermoelastic behaviour of these metamaterials as that of an equivalent homogenous plate. The method provides explicit expressions for the effective thermal properties, which allow for a cost-effective prediction of the thermoelastic response of these metaplates.

Thermoelastic fracture of two-dimensional hexagonal quasicrystal media weakened by a penny-shaped crack subjected to uniformly antisymmetric heat fluxes

This study focuses on the thermoelastic fracture behavior of quasicrystals, a class of solids that exhibit unique properties between traditional crystals and amorphous materials. The complex atomic structure of quasicrystals poses challenges in understanding their fracture mechanisms under thermoelastic loading conditions. Central to our investigation is an analytical examination of a penny-shaped crack in an infinite three-dimensional body composed of two-dimensional hexagonal quasicrystals, where the upper and lower crack surfaces are applied to a pair of uniformly antisymmetric heat fluxes. This crack problem requires simultaneous consideration of thermal-phason-phonon multiple field coupling. According to the symmetry of field variables with respect to the crack plane, the thermal-phason-phonon coupled crack problem is transformed into a mixed boundary value problem in the upper half space. The extended displacement discontinuities, encompassing both phonon and phason displacement discontinuities, as well as the temperature discontinuity, are chosen as the basic unknown variables to construct the boundary integral-differential equations governing the mixed boundary value problem. Based on these boundary governing equations and Fabrikant's potential theory method, the problem with the crack surface subjected to uniform antisymmetric heat fluxes is solved. The solutions of thermal-phason-phonon fields on the crack plane, and in the full space are given in closed-form. Numerical results are employed to validate the obtained analytical solutions and visually illustrate the spatial distribution of thermal-phonon-phason coupling fields in the vicinity of the crack. The study provides fundamental insights into the behavior of cracks in quasicrystals under thermal loading, with potential implications for the design of new materials and structures.

Particle size effect on the thermoelastic behavior of composites—A comparative study between heterogeneous and homogenized beams

The particle size effect on the overall thermoelastic behavior of a composite containing many identical spherical particles reduces with the specimen-particle size ratio (SPR). When SPR is large enough, the effective stiffness converges, and the homogenized properties can represent the composite. This paper addresses two challenging questions: How large of an SPR is enough to reach the convergent results for different loading conditions, and whether is the critical SPR obtained from a uniform loading condition applicable to a nonuniform loading condition? When a uniform load is applied to a composite beam, the elastic moduli and thermal expansion coefficients can be calculated from the material’s response. When the beam is subjected to pure or thermal bending, the deflection can be predicted by the heterogeneous or homogenized beams. The inclusion-based boundary element method (iBEM) is developed for high-fidelity simulation of many-particle systems. Given a volume fraction of particles, particle and beam size, and beam geometry, the local fields and the effective deformation are calculated for uniform and nonuniform loading conditions. The comparative study between a homogenized beam by the micromechanical approach and the numerical simulation of the heterogeneous particle system shows that a much larger SPR is required for thermal bending to reach a convergent result between the heterogeneous and homogenized beam. When the SPR is moderate, a cross-scale modeling method shall replace the micromechanical modeling to achieve accurate results.

Dynamic behavior of the orthotropic hollow cylinder under a magnetic field: a thermoelastic analysis

The present article focuses on the complete analytical solution of an orthotropic hollow cylinder using a proposed magneto-thermoelastic model and finite Hankel transformation. The study considers the Lord–Shulman and Green–Lindsay models of hyperbolic generalized thermoelasticity within the context of thermoelasticity theory. The analytical expressions of the field variables of the cylinder in a magnetic field were obtained under thermo-mechanical loadings. The study also offered closed-form field functions and measured the thermoelastic behavior concerning the magnetic field intensity of the cylinder based on thermoelastic theories involving a second sound. The inclusion of hyperbolic-type heat conduction models enhanced the visualization of the reflection of thermal waves into the cylinder. The study also investigated the impacts of orthotropic material properties on the considered medium and compared the results with the existing literature.

A fully coupled system of generalized thermoelastic theory for semiconductor medium

This study presents a new mathematical framework for analyzing the behavior of semiconductor elastic materials subjected to an external magnetic field. The framework encompasses the interaction between plasma, thermal, and elastic waves. A novel, fully coupled mathematical model that describes the plasma thermoelastic behavior of semiconductor materials is derived. Our new model is applied to obtain the solution to Danilovskaya’s problem, which is formed from an isotropic homogeneous semiconductor material. The Laplace transform is utilized to get the solution in the frequency domain using a direct approach. Numerical methods are employed to calculate the inverse Laplace transform, enabling the determination of the solution in the physical domain. Graphical representations are utilized to depict the numerical outcomes of many physical fields, including temperature, stress, displacement, chemical potential, carrier density, and current carrier distributions. These representations are generated for different values of time and depth of the semiconductor material. Ultimately, we receive a comparison between our model and several earlier fundamental models, which is then graphically represented.

Effects of heat wave propagation and initial stress on the thermo-elastic behavior of porous-auxetic FG circular plate with variable hybrid foundation

Engineering structures' heterogeneity and porous-auxetic features generate some prominent effects on their thermo-mechanical behavior. In addition, initial stress and heat wave propagation also play important roles in the mechanical behavior of FGM structures. Therefore, this paper investigates the effects of heat wave propagation and initial stress on the thermo-elastic behavior of porous-auxetic FG circular/annular plates with variable hybrid foundations. The one-dimensional transient hyperbolic heat conduction equation is modeled using the Cattaneo-Vernotte (C-V) theory and numerically solved using the Crank-sNicolson (C-N) finite difference scheme. Besides, a mathematical model of the other governing equations is extracted based on the classical thermoporoelasticity theory and semi-analytically solved by employing the state-space method and differential quadrature technique. Numerical examples are provided to illustrate the findings of this investigation graphically. The results reveal that the grading indices, and thermal relaxation time have a significant effect on heat wave propagation in the FG circular plate. Initial stress, porosity, and auxeticity also play an important role in its thermoelastic behavior.

Magneto–thermoelastic behavior of an orthotropic hollow cylinder based on Lord–Shulman and Green–Lindsay theories

Magneto–thermoelastic behavior of an orthotropic hollow cylinder based on Lord–Shulman and Green–Lindsay theories

The Thermoelastic Dynamic Response of a Rod Due to a Moving Heat Source under the Fractional-Order Thermoelasticity Theory

In this paper, the thermoelastic behavior of a rod made of an isotropic material under the action of a moving heat source was investigated using a new theory of thermoelasticity related to fractional-order time with two relaxation times. A mathematical model of the one-dimensional thermoelasticity problem was established based on the new thermoelasticity theory. We considered the symmetry of the material, and the fractional-order thermoelasticity control equation was given. Subsequently, the control equations were solved and analyzed using the Laplace transform and its inverse transform. This study examined the effects of fractional-order parameters, time, two thermal relaxation times, and the speed of movement of the heat source on the displacement, temperature, and stress distribution patterns in the rod.

Reedmergnerite and stillwellite-(Ce) from the Dara-i-Pioz alkaline massif: insights into high-temperature behavior of borosilicates

Research subject. Reedmergnerite and stillwellite-(Ce) were obtained from the rocks of the Dara-i-Pioz alkaline massif located on the southern slope of the Alai Range in Tajikistan, which is characterized by the presence of rare mineral species including borosilicates and lithium minerals. Aim. To investigate the thermal behavior of reedmergnerite and stillwellite-(Ce) using high-temperature X-ray diffraction, including the determination of phase transition temperatures and expansion/compression of the unit cell parameters, as well as the calculation of thermal expansion coefficients. Materials and methods. Chemical analysis was performed using a TESCAN MIRA 3 microscope (EDS mode) and a JEOL JXA-8230 electron probe microanalyzer (WDS mode). High-temperature powder X-ray diffraction data were collected using a D8 ADVANCE Bruker diffractometer with an HTK16 heating chamber, covering temperatures from 30°C to 750°C in ambient air. Results. The thermal expansion coefficients of reedmergnerite and stillwellite-(Ce) were determined. Heating reedmergnerite resulted in slight changes in the unit cell parameters, with the parameter c experiencing the smallest change and the parameter a showing the greatest increase. The unit cell volume increased by 1.8% when heated to 750°C and returned to its initial value upon cooling. When stillwellite-(Ce) is heated in the temperature range of 400–450°C, a phase transition occurs, which is confirmed by previously recorded temperature values. The conducted heating and subsequent cooling experiments revealed that the volume and unit cell parameters of stillwellite-(Ce) did not fully revert to their original values. Conclusions. The coefficients of thermal expansion tensor (αij) of rhodmerdgnertite and stillwellite-(Ce) were investigated as a function of temperature using high-temperature in-situ experiments. The phases exhibited relatively low values of thermal expansion parameters compared to the general data for feldspars and borosilicates obtained from literature. These findings contribute to the understanding of the thermoelastic behavior of this group of minerals and their potential applications in various fields.

Nonlinear thermoelastic wave propagation in general FGM sandwich rectangular plates

The present work is dedicated to investigating the thermoelastic wave propagation behavior of sandwich rectangular plates (SRP) made of functionally graded material (FGM). The main contribution lies in the partial modification of basic theoretical expressions and solution methods to improve the accuracy of practical system models. An analytical model with three types of general configurations is established. The porosity distribution in FGM layers depends on the degree of mixture of the constituent materials, with the FGM layers without porosity taken as a reference model. The effect of porosity within FGMs is addressed through a refined analytical formulation of material properties, and the temperature-dependent material properties of FGM sandwich structures (FGMSS) maintain continuity through the thickness. This improved framework introduces a porosity function encompassing three distinct structural and geometrical functions: the core-to-thickness ratio (CTR), porosity volume fraction (PVF), and porosity distribution function (PDF). It is worth mentioning that the theoretical expressions maintain good continuity and reliability under the influence of thermal conditions and system parameters of the proposed structures. Furthermore, considering the generation of thermal strain energy (TSE) caused by thermal expansion of the structure in the normal direction, an improved analytical approach for determining TSE in rectangular plate structures is then investigated by introducing the Green's nonlinear strain (GNS). Hamilton's principle is applied to derive the wave motion equations and analytical solutions for the wave dispersion relations are derived. Furthermore, accurate numerical simulation is performed and the solution is verified with data available in published resources. In addition, we present a systematic parametric analysis to examine the effects of porosity, configuration, power-law exponent (PLE), PVF, CTR, temperature, and wave number on the thermoelastic wave propagation behavior of FGMSRP.

Coupled machine-learning approach and thermoelasticity for analyzing thermal stability of the nanocomposite sandwich system

To offer actionable strategies for mitigating the negative impacts of thermal shock loading and enhancing structural design, this study emphasizes the analysis of the transient coupled thermo-elastic behavior of a sandwich cylindrical panel. This panel is subjected to thermal and heat-flux shocks and features face-layers reinforced by functionally graded graphene platelets (FG-GPLRC) alongside a polymeric core. Leveraging compatibility conditions, a three-layered sandwich structure model is developed. Ensuring calculation precision, the governing equations are formulated based on the comprehensive three-dimensional elasticity theory. A numerical approach is adopted for the analytical solution, targeting the response of both fully simple and clamped-supported setups. The Dubner and Abate method aids in inverting the Laplace transform to ascertain the system’s time evolution. In a subsequent section, the derived results are integrated into a novel machine learning algorithm, the Forest Regression for LAyer-wise Structures (FRAS), to anticipate deflection and stress within the layers. The machine learning outcomes align reasonably well with the multi-layered nature of the structure and diverse regression across layers. This suggests that, for swift preliminary insights in engineering applications, machine learning techniques might be a more efficient alternative to traditional numerical computations.

Crystal chemistry, Raman and FTIR spectroscopy, optical absorption, and luminescence study of Fe-dominant sogdianite

Abstract Fe-dominant sogdianite, a cyclosilicate compound with the chemical formula (Fe3+ 0.74Zr0.64Ti0.46 Al0.15)(□1.02Na0.98)K[Li3Si12O30], was studied. The investigation involved a comprehensive analysis of the mineral sample, including crystal-chemical analysis, Raman and FTIR spectroscopy, optical absorption, and luminescence study. Crystallographic site populations were determined through single crystal structure refinement and electron probe microanalysis. The thermoelastic behavior of a powder was studied using in situ high-temperature X-ray diffraction (30–750 °C). Notably, no phase transition was detected; sogdianite exhibited anisotropic thermal expansion. The first time study of vibrational spectra and spectral bands assigning were performed. The electronic transitions in d 5-ion impurities of sogdianite were studied using optical absorption and luminescence spectroscopy. The origin of pink color and luminescence of sogdianite was clarified. The broad spectral bands in the visible UV spectral region are responsible for the pink color exhibited by sogdianite and could be attributed to d–d transitions occurring in Fe3+ ions.

Acceleration waves in thermoelastic complex media with temperature-dependent phase fields

AbstractWe analyze homothermal acceleration waves in complex materials (those with active microstructure) in the presence of internal constraints that link the temperature to a manifold-valued phase-field describing a generic material microstructure at a certain spatial scale. Such a constraint leads to hyperbolic heat conduction even in the absence of macroscopic strain; we show how it influences the way acceleration waves propagate. The scheme describes a thermoelastic behavior that is compatible with dependence of the free energy on temperature gradient (a dependence otherwise forbidden by the second law of thermodynamics in the traditional non-isothermal description of simple bodies). We eventually provide examples in which the general treatment that we develop applies.

Control of microstructural and mineralogical characteristics on thermo-elastic behaviour of coal-bearing sandstone under mild to high-temperature regimes: Experimental investigation and development of AI prediction models

Control of microstructural and mineralogical characteristics on thermo-elastic behaviour of coal-bearing sandstone under mild to high-temperature regimes: Experimental investigation and development of AI prediction models

Estimation of transverse thermoelastic properties of polyimide fibers based on micromechanical models

The determination of the thermoelastic properties of polyimide (PI) fibers is important for their applications, however, these properties are difficult to measure directly, especially the transverse thermoelastic properties. Here, the transverse thermoelastic properties of PI fibers, including transverse Young's modulus (2.12 GPa), shear modulus (0.94 GPa), Poisson's ratio (0.05), and coefficient of thermal expansion (45.68 μm/m°C), were estimated by combining dynamic and static thermo-mechanical techniques, as well as various relevant micromechanical models. The transverse Young's modulus of PI fibers was only 1/46th of the longitudinal one, and the transverse coefficient of thermal expansion of PI fibers was positive, unlike the longitudinal one, which was negative, showing the typical anisotropy of PI fibers. Finally, the thermoelastic properties of the PI fibers were in turn used to predict the thermoelastic behavior of the PI fiber-reinforced composites, thus validating their effectiveness.

Thermoelastic modeling of cubic lattices from granular materials to atomic crystals

When a cubic lattice is confined by a surface layer, the effective thermoelastic properties can be tailored by the prestress produced by the surface. The thermal expansion coefficient, temperature derivative of elasticity, and the equation of state (EOS) of the solid depend on the potential of each bond and the lattice structure, which can be predicted by the recently developed singum model. This paper first uses a granular lattice confined by a spherical shell to demonstrate singum modeling of the thermoelastic behavior of the cubic lattices and then extends it to atomic crystal lattices by considering the surface tension and long-range interactions. Given the elasticity and the EOS of a cubic crystal, the interatomic potential can be inversely derived. As the bond length changes with thermal expansion and pressure, the singum model predicts the temperature- and pressure-dependent elasticity. Using the orientational average, isotropic elastic constants can be obtained for polycrystals. The case study of copper (Cu) demonstrates the versatility of the model for different cubic lattices and predicts the experimental results of pressure- and temperature-dependent elasticity. The singum model is general for different lattice types and EOS forms and provides clear physical and mechanical meanings to correlate the interatomic potential, EOS, and elasticity in the closed-form formulation, which is very useful in engineering design and analysis of metal structural members in fire, geothermal, and space applications without the needs of large-scale numerical simulations.

A FE Model for the Efficient Simulation of the Thermo-Elastic Machine Tool Behavior

In modern machine tools, the thermo-elastic positioning error has a large share on the overall machine tool error. A multitude of different approaches can be found in the literature to correct this error in order to improve the accuracy of the machine tool. However, an FE-based approach to model the thermo-elastic error of 5 axis machine tools is still an active field of research. Therefore, the goal of this work is the improvement of the machine tool accuracy by modelling the machine tool error using a FE model. The model uses real time measurement data of the thermo-elastic error using an R-Test, as well as real time temperature measurements of the machine structure.

Hybrid stress and heat‐flux formulation of thermodynamics for long‐term simulations in thermo‐viscoplasticity

AbstractIn this article, we present a variational formulation for coupled problems in thermodynamics the most suitable for long‐term simulations of plastic behavior. We start with three‐field Hu–Washize variational formulation and perform regularization to include non‐symmetric stress, we thus recover the formulation that can accommodate any choice of discrete approximation. Such a regularized variational formulation allows us to eliminate the rotation field (as typically less important) and recover the corresponding hybrid stress format for equations of motion and transient heat conduction. The regularized variational formulation is further combined with discrete approximation based upon the Raviart–Thomas vector space for both mechanical and thermal fields, which enforces continuity across element boundaries for stress vector and normal component of heat‐flux. The conservation properties are validated with energy‐conserving scheme for thermoelastic behavior. The time integration of thermo‐viscoplastic behavior is carried out by energy‐decaying scheme to provide superior accuracy for computed stress in a long‐term simulation. The proposed approach offers higher computational robustness and results accuracy than the classical finite elements and time‐integration schemes. Such a performance is illustrated on several numerical simulations in non‐stationary problems for thermo‐viscoplastic behavior.

Fractional heat transfer DPL model incorporating an exponential Rabotnov kernel to study an infinite solid with a spherical cavity

<abstract> <p>The objective of this study was to investigate the thermodynamic reactions of thermoelastic materials by utilizing a modified mathematical fractional thermoelastic model. This model combines a fractional derivative with Rabotnov's exponential kernel and the idea of a two-phase delay, which makes it possible to show thermoelastic behavior more accurately. The model was utilized to investigate an unbounded material with a spherical cavity subjected to a decreasing and shifting heat flux on its inner surface. The problem was solved using analytical approaches, with a strong focus on the Laplace transform. The transform was numerically inverted to provide time-domain results. The study presented graphs that compared the outcomes of utilizing a single kernel fractional derivative with the results obtained using the Rabotnov kernel and fractional order. These graphs showed how the Rabotnov kernel and fractional order affected the physical fields under investigation. This novel theoretical framework has the potential to be advantageous in diverse domains, including engineering, solid mechanics, and materials science.</p> </abstract>