Classical third‐order thermoelastic constants are generally derived from the theory of small‐amplitude acoustic waves in isotropic materials during heat treatments. Investigating higher‐order ...thermoelastic constants for higher temperatures is challenging owing to the involvement of the number of unknown parameters. These Taylor‐type thermoelastic constants from the classical thermoelasticity theory are formulated based on the Taylor series of the Helmholtz free energy density for preheated crystals. However, these Taylor‐type thermoelastic models are limited even at low temperatures in characterizing the temperature‐dependent velocities of elastic waves in solid rocks as a polycrystal compound of different mineral lithologies. Thus, we propose using the Padé rational function to the total thermal strain energy function. The resulting Padé thermoelastic model gives a reasonable theoretical prediction for acoustic velocities of solid rocks at a higher temperature. We formulate the relationship between the third‐order Padé thermoelastic constants and the corresponding higher‐order Taylor thermoelastic constants with the same accuracy. Two additional Padé coefficients α1 ${\mathit{\alpha }}_{1}$ and α2 ${\mathit{\alpha }}_{2}$ can be calculated using the second‐, third‐, and fourth‐order Taylor thermoelastic constants associated with the Brugger's constants, which are consistent with those obtained by fitting the experimental data of polycrystalline material. The third‐order Padé thermoelastic model (with four constants) is validated by the fourth‐order Taylor thermoelastic prediction (with six constants) with ultrasonic measurements for polycrystals (olivine samples) and solid rocks (sandstone, granite, and shale). The results demonstrate that the third‐order Padé thermoelastic model can characterize thermally induced velocity changes more accurately than the conventional third‐order Taylor thermoelastic prediction (with four constants), especially for solid rocks at high temperatures. The Padé approximation could be considered a more accurate and universal model in describing thermally induced velocity changes for polycrystals and solid rocks.
Plain Language Summary
Using the Taylor series for thermoelastic constants at higher temperatures is challenging owing to the involvement of the number of unknown parameters. Thus, we propose the third‐order Padé approximation to replace the Taylor series. Applications to laboratory measurements show that, with much less complexity, the Padé approximation presents a tendency of higher accuracy than the third‐order Taylor series and has similar precision with the higher‐order Taylor series at higher temperatures (up to 1500 K for polycrystals and 1000°C for solid rocks). Then we use such a model to predict the temperature‐dependent velocities of elastic waves. Finally, we analyze the physics of two additional Padé coefficients by associating them with the thermal expansion mismatch due to rock heterogeneities in lithology and with the thermally induced deformation of microcracks.
Key Points
We apply the Padé rational function to the total thermal strain energy function
We correlate the Padé and higher‐order Taylor thermoelastic constants through the equivalency of approximation accuracies
The physics of the Padé coefficients is relevant to the thermal expansion mismatch and thermally induced deformation of microcracks
Current designs of the metastructure can hardly satisfy the demands of the continuous advancement of space exploration. Thus, a new design strategy for the sandwiched metastructure with zero ...thermal-induced warping, high load-bearing capability, and high resonant frequency is urgently needed and provided here. The metastructure composed of three layers: the top plate and the lattice filled sandwiched layer in material I, and the bottom plate in material II. Theoretical models are derived via the flexibility method and fixed-point deformation assumption, revealing the dependences of out-of-plane thermal-induced warping, mechanical-thermal stability, and load-bearing capability on the dominated geometrical parameters of the metastructure. The remarkable agreements among theoretical predictions, FEA results, and experimental measurements provide the accuracy of the theoretical model in predicting structural thermal-induced warping. Compared with the bi-material structure without the interlayer, the sandwiched metastructure exhibits a negligible out-of-plane thermal-induced warping, reduced by 99.8% (i.e., 0.042μm/°C). Additionally, high load-bearing capability (i.e., 0.17GPa) and high resonant frequency (i.e., 532.3Hz) of the metastructure are validated by FEAs and experiments. In summary, this metastructure design can significantly improve the thermal-mechanical stability of functional components of the spacecraft.
•A new design strategy for the sandwiched metastructure with excellent thermal/mechanical properties is proposed.•Theoretical models reveal dependences of thermal/mechanical properties on key geometrical parameters of the metastructure.•The sandwiched metastructure exhibits a negligible out-of-plane thermal-induced warping than the bi-material plate (i.e., 99.8%).•The metastructure shows a high load-bearing capability (i.e., 0.17GPa) and a high resonant frequency (i.e., 532.3Hz).•This design strategy shows its great application prospects in spacecraft and other fields in extreme thermal environments.
•Non-isothermal water transfer is 1D simulated considering 2-phase and CL agglomerate.•The relation in capillary-driven flow and phase-change-induced flow is determined.•Water transport mode in MPL ...and GDL changes with operating conditions.•90% anode RH and 50% cathode RH helps improve PEMFC’s performance and PCI flow.•Thermal strain is unnoticeable compared with the swelling strain induced by inlet RH.
Temperature distribution affects water transport in the porous medium layer of proton exchange membrane fuel cell (PEMFC) by phase-change-induced (PCI) flow. Thus, it is meaningful to reveal the role of PCI flow in removing water. In the present work, a 1-D, non-isothermal, two-phase model is employed to investigate the water transport in cathode gas diffusion layer (GDL) and micro porous layer (MPL). A dimensionless parameter Ts is also proposed to characterize the relation between PCI flow and capillary-driven (CD) flow. It is found that elevating the operating temperature (from 323.15 K to 363.15 K) can facilitate the PCI flow. The high anode and low cathode relative humidity (RHa90%/RHc50%) case contributes to the optimal output performance, corresponding to the largest Ts number and thermal strain. The thermal strain is insignificant compared with the swelling strain and the hygrothermal strain is influenced by the combination of output performance, water distribution and operating conditions. Furthermore, reducing water saturation (sc) at the GDL/gas channel (GC) interface (from 0.12 to 0.0) is conducive to enhancing the proportion of PCI flow in GDL and MPL. By adjusting the operating temperature, inlet RH and removing water at the GDL/GC interface in time enable enhancement of PCI flow and better performance. This work aims to provide a valuable reference for understanding the water transport process and optimizing water management.
This work presents a mesoscopic discrete model of load-induced thermal strain (LITS) as part of the Lattice Discrete Particle Model at high temperature (LDPM-HT) that captures the experimentally ...observed deformations and mechanical responses of concrete heating up to 800 °C under multiaxial loads. In the proposed model, the LITS is decoupled into elastic strain increment due to thermal degradation, and thermo-mechanical strain at the mesoscale. As the most important component, the mesoscopic thermo-mechanical strain is decomposed into a normal and two shear components. The normal component in compression of the thermo-mechanical deformation at the mesoscale controls the macroscopic LITS in the load direction, while the mesoscopic thermo-mechanical strain components in normal tension and shear directions dominate the macroscopic LITS in the unloaded directions. The correctness and accuracy of the improved LDPM-HT are demonstrated by simulating two experimental investigations, namely a heating test up to 800 °C with uniaxial load and a heating test up to 250 °C with multiaxial loads.
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•A discrete model of multiaxial load-induced thermal strain (LITS) is presented.•Model predicts the multiaxial mechanical responses of concrete at high temperature.•Mesoscopic compression thermal strain controls macroscopic LITS in load direction.•Mesoscopic tension-shear thermal strain control macroscopic LITS in unload directions.
•A composite medium with a rigid inclusion under steady or transient thermal loading is studied.•The singular strain and stress at the inclusion tips are identified.•Upper and lower bounds of the ...intensity of the thermal strain are identified.
The problem of a rigid inclusion in an elastic strip under steady or transient thermal loading is studied. The inclusion is assumed to be extremely thin and thermally insulated so that it does not disturb the heat conduction in the strip. The thermal strain and stress fields are obtained by using the singular integral equation technique. The inclusion tip strain and stress are found to be singular. The near tip stresses are expressed in terms of the thermal strain intensity factor. Case studies include the influence of temperature boundary condition, inclusion location and strip width on the thermal strain intensity factor. The highest and lowest values (upper and lower bounds) of the intensity of the thermal strain are identified.
•A large in-plane compressive stress was obtained in the PZT films due to the thermal expansion mismatch of about 88.2 % between the thin films and the steel substrates, which intensifies the ...orientation of the films toward c-axis.•Elemental distribution mapping revealed that a metal-oxide bi-layer in the form of Fe-oxide/Cr-oxide was formed at the interface between the LNO buffer layer and steel substrate and no diffusion or undesired reaction was observed at the PZT/LNO interface.•The sub-10 nm 90° nanodomains were found to be alternately distributed observed along the 001 direction, and the motion of the nanoscale ferroelastic 90° domains is beneficial to the piezoelectric performance.•A large remnant polarization (Pr) of ～67.3μC/cm2 were obtained in the PZT film.
The integration units with functional and structural material components have been developed largely recently. In the present study, 200 nm-thick polycrystalline PbZr0.52Ti0.48O3 (PZT) films with a dense columnar structure were grown on LaNiO3 (LNO) buffered heat-resistant steel substrates via a low-cost chemical solution approach. The behavior of the functional PZT films when combined with the structural steel was investigated mainly by TEM and electrical measurement. A large in-plane compressive stress was obtained in the PZT films due to the thermal expansion mismatch of about 88.2 % between the thin films and the steel substrates, which intensifies the orientation of the films toward c-axis. Sub-10 nm 90° nanodomains were alternately distributed in 001 grains which is beneficial to the piezoelectric performance, and the equivalent d33 value is ～44.4 pm V−1. A remnant polarization (Pr) of ～67.3μC/cm2 and a dielectric constant of ～425 were obtained. The enhanced electrical properties are associated with the stress-induced improved c-axis spontaneous polarization and crystal orientation in the hybrid system. This work may provide a theoretical basis for further integrating functional elements into metallic materials, which is valuable for covering the gap between academic research and industrial mass production.
This paper reports on the high-temperature performance of cementitious materials containing fine glass powders (GP) as a partial replacement for ordinary Portland cement. Various mixes were prepared ...in which cement was replaced by GP in 3 different proportions, i.e., 5 wt%, 10 wt% and 20 wt%. Compressive strength tests were carried out at various temperatures (20, 500 and 800 °C) for mortars containing GP. To have a fundamental understanding of the material behaviour at elevated temperatures, X-ray diffraction (XRD), scanning electron microscopy (SEM) and thermal strain tests were conducted on the corresponding pastes. Results show two distinct temperature ranges regarding effects of GP on the strength of mortars. At temperatures below 500 °C, a mortar mix with 20% GP (Type I) showed the best performance with an average strength loss of 15% compared to 33% strength loss in reference samples. The XRD analysis shows a reduction in the calcium hydroxide (CH) content in mortars with GP. At temperatures below 500 °C, the strength loss is believed to be due to the dehydration of CH. Therefore, the low strength loss of mortars with GP is associated with their low CH content. In the temperature range of 500–800 °C, the average strength loss was 56% in the GP mortar and 35% in the reference mortar. The thermal shrinkage of GP paste is higher than the reference paste. This can be attributed to softening of glasses. The higher strength loss of GP mortar is due to the higher thermal incompatibility which arises because the paste shrinks while sand particles expand.
Light actuation is one of the preferred and advantageous approaches to remotely induce and control deformations in soft materials such as photoactive Liquid Crystal Elastomers (LCEs). Various ...experimental and numerical works have been carried out in the literature to study the actuation of photoactive LCE sheets under illumination. In this study, we have developed a reduced multi-physics model to predict the equilibrium and dynamic response of photoactive LCE beams under illumination. We test our model against an experiment in which a double-clamped thin nematic LCE beam is subjected to UV light, and the stress is generated in the beam due to induced contraction under illumination. Our numerical results demonstrate reasonable agreement with the experiment regarding stress evolution trend and saturation time. We also investigate the bending response of a photoactive LCE beam subjected to UV light. Based on our parameters, we observe that the nematic beam bends towards the light only due to the photochemical strain gradient along the thickness. Finally, to test our model in a dynamic situation, we perform the simulation for the self-oscillations of an LCE beam under illumination. We show that the alternate activation of the top and bottom surfaces of the LCE beam by uniform steady illumination can pump energy into the system, resulting in the phenomenon of self-oscillations.
•Developing a multiphysics model to predict the response of photoactive LCE beam under illumination•Considering both thermal and chemical effects of illumination in the modeling•Generating stress in a double-clamped nematic beam under illumination•Generating self-oscillation in the beam due to alternate illumination of top and bottom surfaces
The Puga geothermal reservoir is located in the south-eastern part of Ladakh (Himalayan region, India), and it is providing encouraging results towards heat production. We proposed an improved ...mathematical model for the fully coupled thermo-hydro-geomechanical model to examine the variations in the Puga geothermal reservoir at between 4500 m from the surface with three, four, and seven hydraulic fractures in the reservoir along with four-spot, five-spot, seven-spot, and nine-spot well patterns. The distribution of low-temperature region is found in each fracture, and it is low in the reservoir with seven hydraulic fractures. The changes in the rock and fluid properties are examined effectively. Thermal strain is dominated in the fractures, and mechanical strain is impressive in the rock matrix; it is dependent on the number of hydraulic fractures and well patterns. The thermal performance of the Puga reservoir is examined with the geothermal life, reservoir impedance, and heat power and found that the number of hydraulic fractures and well patterns are influenced significantly in the multistage modeling of the Puga geothermal reservoir. Thus, the proposed mathematical model can effectively evaluate and predict the variations that occur in the Puga geothermal reservoir with dynamic rock, fracture, and fluid properties.
•Mathematical model improved by including the dynamic variations in the rock, fracture, and fluid properties.•Examined the performance of Puga geothermal reservoir with different well patterns.•Multistage model was proposed to the development of Puga geothermal reservoir.
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