Temperature Gradient Conditions Research Articles

Synthesis of sulfide mineral crystals by incongruent methods using the example of Cu-Fe-S and Cu-Fe-Se systems

Research subject. Understanding the structure and thermodynamic properties of sulfide minerals is important for studying the paragenesis of sulfide formation on Earth and in space, as well as for analyzing technological issues in the processing of ores and polysulfide product concentrates. There is a lack of experimental and theoretical information on many representatives of the Cu-Fe-S and Cu-Fe-Se systems. Aim. To synthesize crystals in the Cu-Fe-S and Cu-Fe-Se systems at the lowest possible temperatures for the subsequent study of their physical properties, while solving the main problem of materials science related to interrelations between composition, structure, and properties. Materials and methods. Crystal synthesis was carried out by the solution-melt method in a stationary temperature gradient, in evacuated sealed quartz glass ampoules. Two types of ampoules were used in the experiment, standard and long. The ampoules were filled with a charge and a salt mixture of RbCl-LiCl of eutectic composition, evacuated and sealed, then placed in several quartz or ceramic glasses. The glasses were placed in tubular furnaces such that the ends of the ampoules with the charge were located closer to the center of the furnace, and the opposite ends were closer to the edge to create a temperature gradient. For standard ampoules, the hot end temperature was 520–469℃, and the cold end was 456–415℃. For long ones: 470℃ – hot end and 340℃ – cold. The synthesis duration ranged from three to four months. Results. Depending on the composition of the charge, crystals of chalcocine Cu2S, bornite Cu5FeS4, chalcopyrite CuFeS2, isocubanite CuFe2S3, and iron-containing dicopper sulfide with an iron content of up to 8 at % and various equilibrium associations with their participation and with the participation of pyrite FeS2 and pyrrhotites Fe1–xS were obtained. Copper dendrites were also found in some samples. In addition, crystals of a phase with the approximate composition of CuFeSe2 were obtained. It is shown that due to different combinations of oxidation states of all three elements dissolved in a salt electrolyte, it is possible to obtain phases with almost any stoichiometric ratio. Chalcopyrite and isocubanite are reliably detected using Raman spectroscopy. In this case, some samples are locally characterized by the “absence” of a spectrum, which probably indicates the metallic (semi-metallic) properties of the samples. Conclusion. Using the Cu-Fe-S and Cu-Fe-Se systems as an example, the possibility of obtaining sulfide crystals in a RbCl-LiCl salt melt up to a eutectic temperature of 313℃ is shown. Due to the low synthesis temperature, the synthesis should be carried out over several months, resulting in crystals a fraction of a millimeter in size.

Influence of Prandtl number on the chaos transition for pure natural and Rayleigh–Bénard convections inside a rectangular cavity

A peculiar flow instability known as multiple chaos transitions was recently reported for the free convection in an enclosure where the direction of the temperature gradient changes continuously; it has been explained to be attributed to the competition for dominance between pure natural and Rayleigh–Bérnard convections. In this study, the chaos transition of free convection is investigated when a horizontal or vertical temperature gradient forms in a rectangular cavity. Analyses are conducted under a laminar flow regime, with Prandtl numbers ranging from 0.01 to 50 and Rayleigh numbers up to 109. In the horizontal temperature gradient, the chaos-transition Rayleigh number increases monotonically with the Prandtl number. However, under vertical temperature gradient conditions, it reaches the maximum value at approximately Pr = 0.5. Contrary to the general knowledge that higher-Prandtl number fluids effectively stabilize natural convection, a free convection in a vertical temperature gradient initiates a new flow instability when the Prandtl number is over 1.0, where momentum and thermal diffusions balance each other. The oscillation pattern, 2D phase trajectory, power spectral density, and Poincaré point of equivalent thermal conductivity are used to assess the free-convection flow instability.

Experimental study on the influence of inlet pressure on the flow parameters at the reverse flow boundary of vortex tube and its relation with energy separation performance

The performance of the vortex tube (also known as the Ranque-Hilsch tube) is significantly influenced by the inlet pressure and the internal flow processes, which can be categorized into two distinct flows: the center and the outer flow. The reverse flow boundary, acting as the interface between the two flows, plays a crucial role in energy separation. However, the research on the location of the reverse flow boundary and the associated flow parameters and energy transfer at this boundary are still insufficient. Therefore, this research employs the measurement method of interpolation probe to analyze the distribution of the reverse flow boundary and the specific flow parameters at this boundary. These parameters include static pressure gradient, angular velocity, and static temperature gradient, which substantially impact energy separation. A qualitative analysis of the energy transfer process in the vortex tube by examining mass flow in the reverse area and tangential and axial velocities are further delved. This analysis covers momentum transfer, heat transfer, and turbulent heat transfer processes resulting from the compression and expansion processes. The findings provide a research direction for exploring the energy separation performance of vortex tubes.

Experimental re-melting of a continental crust: probing the deep storage zone of Campi Flegrei and Vesuvius magmas

Mantle magmas interact with surrounding rocks during their ascent and storage in the continental crust, leading to open system processes as wall rock partial melting. In this study, we have experimentally investigated the reactions between a leucosome depleted migmatite and a primitive K-basaltic of Campi Flegrei (Italy). Experiments were carried out at pressure of 0.8 GPa temperatures from 1250 °C to 1050 °C and constant temperature and thermal gradient conditions. The experimental products consist of biotite-free migmatite, glass and crystals of clinopyroxene, olivine, plagioclase and Cr-spinel with proportions that vary as a function of temperature. Open system isothermal experiments indicate that the chemistry of melts and phase relationships are controlled by the high Al2O3 content of leucosome depleted migmatite with the glass composition shifting from K-trachybasalt towards shoshonite as the temperature decreases from 1200 °C to 1125 °C. At temperatures \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\le$$\\end{document}1150°C, migmatite assimilation is not exclusively due to the assimilation fractional crystallization process because evidence of mingling and mixing is observed. T-gradient experiment shows melt composition ranging from shoshonite to phono-tephrite moving from the slightly crystalline zone (T = 1250 –1210 °C) at the bottom of the capsule towards the highly crystalline zone (T = 1160 –1140 °C). This SiO2-constant trend indicates that at temperature below the basalt solidus, the assimilation of leucosome depleted crust is represented almost exclusively by the biotite breakdown, leading to the increase in Al, Mg, Fe, Ti, and K activities in the system. The shoshonitic composition obtained in our experiments could represent the parental magma for both Campi Flegrei volcanic district and Vesuvius magmatic systems, indicating modification in a deep storage zone through mixing with the partial melts derived from restitic continental crust.

Nitrate denitrification rate response to temperature gradient change during river bank infiltration.

Nitrate attenuation during river bank infiltration is the key process for reducing nitrogen pollution. Temperature is considered to be an important factor affecting nitrate attenuation. However, the magnitude and mechanism of its impact have not been clear for a long time. In this study, the effects of temperature and temperature gradient on the nitrate denitrification rate were investigated via static batch and dynamic soil column simulation experiments. The results showed that temperature had a significant effect on the denitrification rate. Temperature effects were first observed in denitrifying bacteria. At low temperatures, the microorganism diversity was low, resulting in a lower denitrification rate constant. The static experimental results showed that the denitrification rate at 19°C was approximately 2.4 times that at 10°C. The dynamic soil column experiment established an exponential positive correlation between the nitrate denitrification decay kinetic constant and temperature. The affinity of denitrifying enzymes for nitrate in the reaction substrate was ordered as follows: decreasing temperature gradient (30°C → 10°C) > zero temperature gradient (10°C) > increasing temperature gradient condition (0°C → 10°C). This study provides a theoretical basis for the biogeochemical processes underlying river bank infiltration, which will help aid in the development and utilization of groundwater resources.

Numerical simulation of temperature gradient effects on gallium nitride crystal growth by sodium-flux method

During the growth of gallium nitride single crystals by sodium-flux method, temperature significantly impacts crystal quality. In this study, the mechanism of the effect of different temperature gradients on crystal growth is analyzed in depth using a combination of numerical simulation and experiment. The experimental results show that epitaxial growth of crystals occurs under positive temperature gradient conditions, while there is dissolution of seed crystals under negative temperature gradient conditions. The temperature, flow, and concentration data of the melted material during crystal growth were calculated using numerical simulation. The simulation findings reveal that the distribution of solution supersaturation varies according to temperature. High supersaturation at the bottom of the melt is favorable for crystal epitaxial growth on the surface of seed crystals under a positive temperature gradient. Meanwhile, low supersaturation at the top of the melt suppresses the hard polycrystalline layer here. Under negative temperature gradient conditions, low supersaturation at the bottom of the melt may lead to remelting of seed crystals, which is consistent with the experimental phenomenon. Furthermore, we propose an optimized heat source profile. This profile manages high supersaturation near seed crystals, aiding continuous growth. Finally, we have applied the curve in an applied way by proposing a multi-stage heating device, based on which the desired arbitrary temperature profile can be modulated. This research has broad applications in a variety of crystal growth experiments using fluid as the mother phase.

Computational Model of Effective Thermal Conductivity of Green Insulating Fibrous Media.

Modelling effective thermal properties is crucial for optimizing the thermal performance of materials such as new green insulating fibrous media. In this study, a numerical model is proposed to calculate the effective thermal conductivity of these materials. The fibers are considered to be non-overlapping and randomly oriented in space. The numerical model is based on the finite element method. Particular attention is paid to the accuracy of the results and the influence of the choice of the representative elementary volume (REV) for calculation (cubic or rectangular parallelepiped slice). The calculated effective thermal conductivity of fibrous media under different boundary conditions is also investigated. A set of usual mixed boundary conditions is considered, alongside the uniform temperature gradient conditions. The REV rectangular slice and uniform temperature gradient boundary conditions provide a more accurate estimate of the effective thermal conductivity and are therefore recommended for use in place of the usual cubic representative elementary volume and the usual mixed boundary conditions. This robust model represents a principal novelty of the work. The results are compared with experimental and analytical data previously obtained in the literature for juncus maritimus fibrous media, for different fiber volume fractions, with small relative deviations of 7%. Analytical laws are generally based on simplified assumptions such as infinitely long fibers, and may neglect heat transfer between different phases. Both short and long fiber cases are considered in numerical calculations.

Mass transfer in the snow strata under conditions of large temperature gradients

In the winter of 2022-2023, a study of the crystal structure of hoarfrost horizons on the slopes of Mount Elbrus was carried out in conditions of the low-snow winter period. By means of a digital portable microscope the data were obtained, according to which, the average size of crystals of hoarfrost is 1.5- 2.5 mm, and the most frequent form of crystals of hoarfrost is flat skeletal, columnar faceted and columnar semi-skeletal forms. The study confirmed the previously observed regularity that mass transfer in the snow column depends on the magnitude of the temperature gradient, the degree of water vapor saturation in the transit zones which, among other things, are influenced by the snow cover thickness and absolute height.

Thermomechanical modeling of dissimilar-material interfaces in composite structures

Due to the heterogeneities in material properties of strongly-bonded multi-material composite structures, there exist singularities of the stress fields at the material interface as well as the interface corners on the bounding surfaces. The finite-element method is probably the only plausible option to analyze the stress around such interfaces between dissimilar materials subjected to combined thermo-mechanical loading. In this article, we propose a novel mathematical model for the computational analysis of coupled thermo-elastic fields with perfectly bonded interfaces of dissimilar isotropic/orthotropic composite-material structures. A scalar function of the spatial variables, namely, the displacement function, is used to integrate the temperature field and the associated displacement-function field to obtain two nonhomogeneous partial-differential equations of equilibrium that govern two thermo-mechanical sub-problems defined in terms of the appropriate conditions of orthogonal temperature gradients. For a specific temperature field, obtained as a steady-state solution of the given thermal problem, the two thermo-mechanical sub-problems are solved independently to obtain the full-field solution of the thermo-elastic problem using the method of superposition. As an alternative to the conventional computational approach, we employed a single variable semi-analytical method of solution to determine the thermo-mechanical response of the multi-material composite structures. The continuity of the temperature and the heat flux in the thermal field problem and the continuity of the displacement and the traction vectors are utilized in the elastic field problem to determine the appropriate algebraic equations suitable for nodal application at the interfaces as well as interface corners on the boundaries of the respective problems. The quantitative comparison of the present displacement-function solutions to several mixed-boundary-value problems with those obtained by the conventional finite-element method verifies the high accuracy and effectiveness of the present method. This computational model has potential applications in identifying near-interface high-stress locations as well as possible critical regions of the physical boundary of composite structures subjected to mixed modes of thermal and mechanical loadings.

Compositional Grading of Al<sub>2</sub>O<sub>3</sub>/ZrO<sub>2</sub>/SUS304 Hybrid Materials Using Centrifugal Slurry Methods and Spark Plasma Sintering

Ceramic/ metal functionally graded materials (FGMs) have been promising to sustain coating structures working under super high temperature as well as high temperature gradient conditions. Compositional gradients in the FGMs can be engineered according to functional performance requirements. This study aims to fabricate Al2O3/ZrO2/SUS304 hybrid FGMs with continuous compositional gradient manners using a combination of centrifugal slurry methods and spark plasma sintering (SPS). The compositional gradients in the FGMs were investigated on microstructures with elemental distributions and hardness on the cross sections of the FGMs. It was demonstrated that the compositions of ZrO2 and SUS304 continuously varied in the FGMs, while Al2O3 resided only on ZrO2-rich sides, which can effectively enhance the fracture toughness of the ZrO2-rich layer. Ball milling treatments can make the Al2O3 layer more formed in the ZrO2-rich layer. With increasing the amount of Al2O3, the Al2O3 layer resided closer to the top of the ZrO2 surfaces in the FGMs subject to ball milling treatments, which can prevent the crack propagation from the ZrO2 top surfaces.

Features of Structures and Ionic Conductivity of Na3Fe2(PO4)3 Polycrystals Obtained by Solid Phase and Melt Methods

This article investigates the structures and conductive properties of polycrystals of Na3Fe2(PO4)3 obtained by solid-state and melt synthesis methods using concentrated optical radiation. It has been established that in the melt synthesis method, the material is synthesized under significantly non-equilibrium thermodynamic conditions, leading to the creation of deformations in the sample, which contribute to the enhancement of ionic conductivity. Additionally, the synthesis duration is reduced by half. Through a comparative assessment of the structural parameters and conductive properties of these materials, it is demonstrated that polycrystals obtained by the melt method exhibit better texture and higher ionic conductivity. The occurrence of deformations during the synthesis of α-Na3Fe2(PO4)3 under high temperature-gradient conditions indicates the elasticity of the crystalline framework {[Fe2(PO4)]3−}3∞. It is concluded that the non-equilibrium thermodynamic conditions of α-Na3Fe2(PO4)3 synthesis promote the formation of deformations in the crystalline structure of polycrystals, leading to a partial increase in symmetry and ionic conductivity.

Nonlinear vibration characteristics of elastically supported FRP cylindrical shells under temperature gradient conditions: Theoretical and experimental studies

The nonlinear free vibrations of elastically supported fiber-reinforced polymer cylindrical shells (FRPCSs) under temperature gradient conditions are investigated using both theoretical and tested techniques. A dynamic model of the FRPCSs with consideration of such complex thermal conditions is firstly established based on the first-order shear deformation theory in conjunction with Hamilton’s principle, the Galerkin method, the artificial spring technique, etc. Numerical results at room temperature and in a uniform thermal environment with classical or arbitrary boundary conditions are utilized to give a rough validation of this model. Subsequently, a thermal-vibration system is set up to measure the nonlinear natural frequencies of two FRPCS specimens subjected to four different temperature gradient conditions in free-free boundary constraints, and iterative calculations are performed to identify the temperature-dependent material properties. Finally, the detailed comparisons of calculated and experimental results provide a solid validation of the proposed model. This study offers a practical model tool to forecast the nonlinear free vibrations of the FRPCSs in a complex thermal environment, which can be readily adjusted and extended to other forms of composite shells. Also, the predicted and measured results can help assess the structural thermal-vibration behaviors when the temperature gradient effect needs to be considered. Communicated by Makoto Ohsaki.

Development of in-situ Delayed Hydride Cracking tests using neutron imaging to study the H redistribution in Zr-2.5%Nb

Delayed Hydride Cracking (DHC) is a failure mechanism that occurs in Zr alloys under certain conditions of hydrogen concentration, temperature and stress gradient. In service, hydrogen produced by corrosion reaction can be incorporated in Zr alloys and if the solid solubility is exceeded, hydrogen precipitates as zirconium hydride. The presence of a stress concentrator, such as a crack, generates the hydrogen diffusion and precipitation to the high stress zone beginning the DHC process. In this work, in-situ DHC tests in air at 250°C were performed at ANTARES, the neutron imaging facility of the FRM-II reactor. Samples of Zr2.5%Nb produced from extruded tubes and pressure tubes were studied using a stress rig specially modified to perform DHC tests in the neutron beam. H redistribution during mechanical testing was followed in-situ by registering the changes in neutron transmission. The results were compared with the images obtained by light optical microscopy after the tests. The results highlight the capabilities of neutron imaging to analyze time-dependent H distribution during DHC crack growth.

Energy transport between heat baths with oscillating temperatures.

Energy transport is a fundamental physical process that plays a prominent role in the function and performance of myriad systems and technologies. Recent experimental measurements have shown that subjecting a macroscale system to a time-periodic temperature gradient can increase thermal conductivity in comparison to a static temperature gradient. Here, we theoretically examine this mechanism in a nanoscale model by applying a stochastic Langevin framework to describe the energy transport properties of a particle connecting two heat baths with different temperatures, where the temperature difference between baths is oscillating in time. Analytical expressions for the energy flux of each heat bath and for the system itself are derived for the case of a free particle and a particle in a harmonic potential. We find that dynamical effects in the energy flux induced by temperature oscillations give rise to complex energy transport hysteresis effects. The presented results suggest that applying time-periodic temperature modulations is a potential route to control energy storage and release in molecular devices and nanosystems.

Assessing the feasibility of assisted migration of corals in the Red Sea

Climate change, and in particular the unprecedented rapid global warming, presents a major threat to corals, with warming rates potentially exceeding the adaptive capacities of most coral species. Assisted gene flow, the human facilitated introduction of temperature resilience alleles from warmer to threatened colder populations via the movement of individuals (assisted migration) or their gametes (selective breeding), has been suggested as a tool to transfer thermal adaptations among populations. Due to its strong latitudinal temperature gradient and extreme temperature conditions, the Red Sea constitutes an ideal location to investigate the potential of this strategy. Here, we relocated Porites lobata colonies from three reefs along the Saudi Arabian Red Sea with different mean sea surface temperature summer maxima (ranging from 30.9 °C in Duba, 32.5 °C in Thuwal, to 33.8 °C in Jazan) to a common garden experiment in the intermediate central location. Five colonies from each location were fragmented and deployed in situ in early summer of 2018 to investigate physiological differences in bleaching, survival, and growth. Results showed significantly higher bleaching in fragments from Duba, followed by 65% mortality. Even though no bleaching was observed in fragments from Jazan, mortality rates of around 20% indicated that other environmental parameters besides temperature might influence coral health and survival. These results suggest that assisted gene flow via translocation alone may be restricted in its success due to a lack of local adaptations to environmental conditions other than temperature. However, strategies like inter-populational breeding may overcome these limitations as they might allow producing offspring with both increased thermal tolerance and local adaptations.

Carbon Dioxide Concentration Estimation in Nonuniform Temperature Fields Based on Single-Pass Tunable Diode Laser Absorption Spectroscopy.

We propose a novel technique to accurately predict carbon dioxide (CO2) concentrations even in flow fields with temperature gradients based on a single laser path absorption spectrum measurement and machine learning. Concentration measurements in typical tunable diode laser absorption spectroscopy are based on a ratio of two integrated absorbances, each from a spectral line with different temperature dependence. However, the inferred concentrations can deviate significantly from the actual concentrations in the presence of temperature gradients. Furthermore, it is also difficult to find an analytical expression to compensate for the effect of nonuniform temperature profiles on concentration measurements. In this study, the entire absorption feature was considered since its shape and peak intensities vary with temperature and concentration. Specifically, a predictive model is obtained in a data-driven manner that can identify and compensate for the effect of a nonuniform temperature field on the spectrum. Despite a very detailed understanding of the CO2 absorption spectrum, it is nearly impossible to collect sufficient spectra for model acquisition by varying all temperature gradient conditions. Therefore, the model was obtained using only simulated data, much like the concept of a "digital twin". Finally, the predictive performance of the acquired model was verified using experimental data. In all test cases, the predictive performance of the model was superior to that of the two-line method. Additionally, a gradient-weighted regression activation mapping analysis confirmed that the model utilizes both the peak intensities as well as the change in the shape of absorption lines for prediction.

Study on the morphology of liquid–gas interface inside inertial confinement fusion target under the condition of temperature gradient based on Young–Laplace equation

This study investigates the morphology of the liquid–gas interface inside inertial confinement fusion targets with temperature gradients from the perspective of force balance. The effects of contact angle, liquid volume, temperature gradient, and target size on the interface morphology are discussed. The filling of the fuel and the preparation of the ice layer inside the target are carried out near the deuterium–deuterium triple point at 18.71 K, accompanied by temperature gradient distributions of different magnitudes. The morphology of the liquid–gas interface has a significant impact on the subsequent laser experiments. The differential equation for calculating the morphology of the liquid–gas interface under non-uniform temperature field is derived based on the Young–Laplace equation. In order to verify the accuracy and applicability of the model as well as to provide guidance for practical applications such as process optimization, experimental data within a temperature gradient range of 0.69–1.38 K/cm during the fuel filling process were selected. Image processing techniques, including denoising and edge detection, were applied to the experimental images. The obtained structured data were compared with the numerical solutions of the equation for the liquid–gas interface morphology. The accuracy of the equation was verified by the results. Based on this, the morphology of the liquid–gas interface of deuterium–deuterium inside targets under different experimental conditions was calculated. It was found that a smaller target radius, higher filling temperature, smaller contact angle, and larger temperature gradient are more conducive to subsequent experiments.

In situ measurement of full-field deformation for arc-based directed energy deposition via digital image correlation technology

Deformation measurement and control is a critical challenge in metal additive manufacturing. The metal deposition and solidification occur under the condition of high temperature gradient and large restriction accompany with complex metallurgical phenomena and stress evolutions. High stresses may result in deformation over yield strength of material, or even crack and fracture over the ultimate strength. Thus, it is necessary to monitor the deformation during additive manufacturing process. This paper focus on an in situ measurement of full-field deformation for arc-based directed energy deposition process via digital image correlation (DIC) technology. The measurement qualities were evaluated from the following aspects including system error, speckle pattern, influence of arc light and comparison in 2D-DIC and 3D-DIC. Results indicated that the relative system error of the measured deformation is no more than 0.12 % within a total deformation of 12 mm. Both the artificial speckle and natural speckle can meet the requirement of 2D-DIC system. The image qualities for artificial speckle is higher than that of natural speckle. For 3D-DIC, however, artificial speckle must be applied. The moving arc light will weaken the image qualities, which must be shielded in order to prevent the interference of intense light and the damage of speckle. An L-type shield was proposed and proved to be practical. Finally, DIC measuring was applied in both single-wall and cylindrical AM parts, comparing with numerical simulation. Results indicated that the evolution of the measured deformations showed good agreement with that of numerical simulation. Deformation evolution mechanism was revealed through numerical simulation and the evolution process was divided into three stages. For the cylindrical part, the final outer contour measured by DIC was consistent with that of 3D laser scanning and numerical simulation. As a conclusion, DIC technology was proved to be a feasible approach for in situ monitoring of full-field deformation of arc-based directed energy deposition process.

A temperature gradient test system for investigating thermo-mechanical responses of containment materials of underground storage facilities

Underground energy storage is a promising option for the global ambition of moving towards carbon neutrality. To achieve safe and reliable energy storage in underground caverns, it is essential to understand the contributions of thermal and mechanical loads to the deformation of containment materials (e.g., concrete and geomaterials) and to forecast potential risks related to unexpected failure of these materials. A temperature gradient test system is developed to investigate the thermo-mechanical responses of containment materials under simulated temperature gradient and earth pressure conditions. The test system has advantages of establishing a temperature gradient of over 400 ​°C/m across a large-scale specimen and examining the resulting strain based on the digital image correlation analysis. This study sheds light on 3 typical applications of the test system to examine the thermal and mechanical responses of intact limestone, flawed limestone, and fractured concrete. The results demonstrate that the mechanical load mainly controls the strain evolution of the intact limestone, while the thermal load strongly affects the strain evolution around the circular hole. The failure pattern of concrete primarily influences the mechanically induced strain, and the thermally induced strain is insensitive to the concrete failure. This test system can be modified and upgraded to study various research topics related to underground energy storage.

Physically informed deep homogenization neural network for unidirectional multiphase/multi-inclusion thermoconductive composites

Elements of the periodic homogenization framework and deep neural network were seamlessly connected for the first time to construct a new micromechanics theory for thermoconductive composites called physically informed Deep Homogenization Network (DHN). This method utilizes a two-scale expansion of the temperature field of spatially uniform composites in terms of macroscopic and fluctuating contributions. The latter is estimated using deep neural network layers. The DHN is trained on a set of collocation points to obtain the fluctuating temperature field over the unit cell domain by minimizing a cost function given in terms of residuals of strong form steady-state heat conduction governing differential equations. Novel use of a periodic layer with several independent periodic functions with adjustable training parameters ensures that periodic boundary conditions of temperature and temperature gradients at the unit cell edges are exactly satisfied. Automatic differentiation is utilized to correctly compute the fluctuating temperature gradients. Homogenized properties and local temperature and gradient distributions of unit cells reinforced by unidirectional fiber or weakened by a hole are compared with finite-element reference results, demonstrating remarkable correlation but without discontinuities associated with temperature gradient distributions in the finite-element simulations. We also illustrate that the DHN enhanced with transfer learning provides a substantially more efficient and accurate simulation of multiple random fiber distributions relative to training the network from scratch.