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Search Results (1,845)

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Keywords = theory of elasticity

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29 pages, 5712 KB  
Article
Load Characteristics and Friction Torque Analysis of Triple-Row Wheel Hub Bearings
by Wei Xiong, Guilai Zheng, Haibo Zhang, Min Yu and Xiaomeng Wang
Lubricants 2026, 14(1), 45; https://doi.org/10.3390/lubricants14010045 - 20 Jan 2026
Abstract
Aiming at analyzing the load characteristics and friction torque of triple-row hub bearings for new energy vehicles, this work established a comprehensive theoretical and experimental methodology for predicting the internal load distribution and friction torque. Firstly, considering the preload effect via an initial [...] Read more.
Aiming at analyzing the load characteristics and friction torque of triple-row hub bearings for new energy vehicles, this work established a comprehensive theoretical and experimental methodology for predicting the internal load distribution and friction torque. Firstly, considering the preload effect via an initial negative clearance, deformation coordination and force balance equations for the triple-row bearing under axial load were formulated, to analyze the external loads under various driving conditions. Based on contact deformation theory, a quasi-static model was developed to combine radial, axial, and moment loads. The Newton–Raphson iterative algorithm was employed to solve the ball load distribution equations, and the correctness was verified by using the finite element method. Furthermore, accounting for the elastic hysteresis, differential sliding, and spin sliding, the theoretical models for friction torque components were established, to investigate the influence of structural parameters and the total friction torque under different driving conditions. Finally, to confirm the effectiveness and the precision of the model, a finite element simulation and experimental measurements of friction torque were conducted, respectively, which showed good agreement with theoretical calculations. The main innovations include proposing a mechanical modeling method for triple-row hub bearings that accounts for preload effects, and establishing an integrated friction torque analysis model applicable to multiple driving conditions. This work provides theoretical support and a methodological foundation for the design of next-generation hub bearings for new energy vehicles. Full article
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32 pages, 13039 KB  
Article
Freeze-Thaw Behavior and Damage Prediction of Mixed Recycled Coarse Aggregate Concrete
by Huaiqin Liu, Jiale Chen, Ping Zhang, Weina Li, Wei Su, Tian Su, Shangwei Gong and Bangxiang Li
Buildings 2026, 16(2), 368; https://doi.org/10.3390/buildings16020368 - 15 Jan 2026
Viewed by 136
Abstract
To address the freeze-thaw (F-T) durability of concrete structures in severely cold plateau regions, this study investigates recycled coarse aggregate concrete (RCAC) by designing mixtures with varying replacement ratios of recycled brick aggregate (RBA). Rapid freeze-thaw cycling tests are conducted in combination with [...] Read more.
To address the freeze-thaw (F-T) durability of concrete structures in severely cold plateau regions, this study investigates recycled coarse aggregate concrete (RCAC) by designing mixtures with varying replacement ratios of recycled brick aggregate (RBA). Rapid freeze-thaw cycling tests are conducted in combination with macro- and microscale analytical techniques to systematically elucidate the frost resistance and damage mechanisms of mixed recycled coarse aggregate concrete. When the RBA content is 50%, the concrete demonstrates relatively better frost resistance within the mixed recycled aggregate system. This is evidenced by the lowest mass loss rate coupled with the highest retention ratios for both the relative dynamic elastic modulus (RDEM) and the compressive strength. Micro-analysis indicates that an appropriate amount of RBA can optimize the pore structure, exerting a “micro air-cushion” buffering effect. Blending RBA with recycled concrete aggregate (RCA) may create functional complementarity between pores and the skeleton, effectively delaying freeze–thaw damage. A GM (1,1) damage prediction model based on gray system theory is established, which demonstrates high accuracy (R2 > 0.92). This study provides a reliable theoretical basis and a predictive tool for the durability design and service life assessment of mixed recycled coarse aggregate concrete engineering in severely cold regions. Full article
(This article belongs to the Special Issue Low-Carbon Materials and Advanced Engineering Technologies)
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16 pages, 1476 KB  
Article
Evaluating the Effects of Pore Tortuosity on the Propagation of Compressional Waves in Saturated Soils
by Xueying Chu, Guohui Lei and Xin Zhao
Appl. Sci. 2026, 16(2), 858; https://doi.org/10.3390/app16020858 - 14 Jan 2026
Viewed by 71
Abstract
In the wave theory of saturated soils, pore tortuosity is an important physical property for quantifying the added mass force caused by the relative acceleration between solid and liquid phases. However, this inertial force is often ignored for simplicity in practical applications. To [...] Read more.
In the wave theory of saturated soils, pore tortuosity is an important physical property for quantifying the added mass force caused by the relative acceleration between solid and liquid phases. However, this inertial force is often ignored for simplicity in practical applications. To investigate the influence of pore tortuosity on the propagation of compressional waves in saturated soils, a system of generalized governing equations for one-dimensional infinitesimal strain elastic waves is solved using the Laplace transform method. Semi-analytical solutions are obtained for the spatiotemporal distributions of the excess pore water pressure, the pore water velocity, and the soil particle velocity caused by a step load perturbation under undrained conditions. These solutions are used to evaluate the effects of pore tortuosity on the velocities and amplitudes of fast and slow compressional waves. The results show that pore tortuosity has an insignificant effect on the propagation of fast compressional waves, but for slow compressional waves, the larger the pore tortuosity is, the lower the wave velocity and the larger the wave amplitude. Ignoring the influence of pore tortuosity can lead to an underestimation of the arrival time of slow compressional wave. The propagation of this wave is limited to a distance of approximately 1 m away from the loading boundary. This research finding is purely theoretical. For further experimental validation, it is suggested to detect the slow compressional wave by placing miniature acoustic receiving transducers as close as possible to the loading or transmitting surface. The proposed solutions are also useful for calibrating sophisticated numerical codes for dynamic consolidation of saturated soils and wave transmission in porous media. Full article
(This article belongs to the Special Issue Latest Research on Geotechnical Engineering—2nd Edition)
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24 pages, 3791 KB  
Article
Two-Stage Assumed Mode Method for Flutter Analysis of Supersonic Panels with Elastic Supports and Attached Masses
by Wuchao Qi, Shuai Yuan and Sumei Tian
Aerospace 2026, 13(1), 89; https://doi.org/10.3390/aerospace13010089 - 14 Jan 2026
Viewed by 119
Abstract
During the service life of a supersonic aircraft, panels are susceptible to damaged boundary supports and unexpected attached masses, which can critically alter their flutter characteristics. This paper proposes a novel two-stage assumed mode method to efficiently analyze the modal properties and expanded [...] Read more.
During the service life of a supersonic aircraft, panels are susceptible to damaged boundary supports and unexpected attached masses, which can critically alter their flutter characteristics. This paper proposes a novel two-stage assumed mode method to efficiently analyze the modal properties and expanded flutter envelopes of such compromised structures. In the first stage, the bending modes of a Euler–Bernoulli beam under elastic supports in two orthogonal directions are combined to construct the assumed modes of the intact panel, forming a modal matrix that satisfies geometric boundary conditions and establishing the baseline dynamic model. In the second stage, the method is reapplied to derive the generalized eigenvalue problem for the panel with attached masses, accurately capturing the modified mode shapes and frequencies. Subsequently, based on the principle of virtual work and first-order piston theory, the generalized aerodynamic forces are formulated. These are then incorporated into the flutter equations, which are solved in the frequency domain using the p-k method. The results demonstrate that elastic supports generally lower flutter velocities and frequencies. However, an interesting finding is that a centrally attached mass of 0.03 kg (≈10% of the panel mass) can increase the flutter speed by about 10%, whereas the same mass placed off-center may reduce it by roughly 2%. Furthermore, the proposed 9-point damper layout is shown to raise the flutter speed of an elastically supported panel with an off-center mass by up to 18% and the flutter frequency by over 13%, thereby recovering and even exceeding the design flutter boundary. Full article
(This article belongs to the Special Issue Aeroelasticity, Volume V)
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15 pages, 13053 KB  
Article
Development of Ti-Nb-Mo-Zr Alloys with Low Modulus and Excellent Plasticity for Biomedical Applications
by Sen Yang, Zhiyuan Jia, Xueyan Song, Junyang He and Xiaoyong Zhang
Materials 2026, 19(2), 325; https://doi.org/10.3390/ma19020325 - 13 Jan 2026
Viewed by 321
Abstract
Metastable β titanium alloys with low elastic modulus and excellent plasticity represent highly attractive materials for biomedical stent application. Our work shows that Zr plays a crucial role in regulating β stability to significantly reduce the modulus and enhance plasticity. A series of [...] Read more.
Metastable β titanium alloys with low elastic modulus and excellent plasticity represent highly attractive materials for biomedical stent application. Our work shows that Zr plays a crucial role in regulating β stability to significantly reduce the modulus and enhance plasticity. A series of Ti-25Nb-2Mo-xZr (x = 0, 3, 9, 12 wt%) alloys were designed based on the d-electron theory, and the influence of Zr content on the microstructure, mechanical properties, and deformation mechanism were systematically investigated. The results demonstrated that as the Zr content increases, the β phase stability was significantly enhanced. This leads to, first, the suppressed formation of the high modulus α″ phase and ω phase, which results in the decrease in apparent overall elastic modulus. Second, the dominant mode of deformation shifts from martensite dislocation slip (0Zr) to martensitic variant reorientation (3Zr), then to stress-induced martensite transform (SIMT, 9Zr), and finally to a combination of SIMT and deformation twinning (12Zr). Such shifting effectively increases the alloy’s tensile plasticity. Among the series, the Ti-25Nb-2Mo-12Zr alloy exhibited the lowest elastic modulus of 56.3 GPa, together with the highest elongation to failure of 48.2%, demonstrating that the alloy possesses considerable potential for biomedical applications. Full article
(This article belongs to the Special Issue Research on Performance Improvement of Advanced Alloys (2nd Edition))
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14 pages, 3415 KB  
Article
Drilling Performance Experiment and Working Load Modeling Calculation of Diamond Coring Bit
by Jianlin Yao, Bin Liu, Kunpeng Yao and Haitao Ren
Processes 2026, 14(2), 267; https://doi.org/10.3390/pr14020267 - 12 Jan 2026
Viewed by 187
Abstract
Diamond coring bits exhibit stable rock-breaking and coring processes as well as a long service life. However, when drilling in complex and challenging formations are characterized by high hardness, strong plasticity, and high abrasiveness, issues such as low rock-breaking efficiency, rapid failure, and [...] Read more.
Diamond coring bits exhibit stable rock-breaking and coring processes as well as a long service life. However, when drilling in complex and challenging formations are characterized by high hardness, strong plasticity, and high abrasiveness, issues such as low rock-breaking efficiency, rapid failure, and shortened service life frequently occur. To prevent premature bit failure and enhance rock-breaking efficiency, this study investigated the effects of drilling pressure and rotational speed on rock-breaking performance through bench-scale experiments using typical rock samples. A total of 15 experimental groups were included in this study, with one independent trial performed for each group. ROP is calculated as the ratio of effective drilling depth to time consumed, and MSE is derived based on axial force, torque, and rock-breaking volume. The experimental results indicated that (1) sandstone is more sensitive to rotational speed, whereas limestone and dolomite are more sensitive to drilling pressure; (2) the minimum mechanical specific energy (MSE) of sandstone was achieved at a drilling pressure of 15 kN and rotational speed of 50 r/min; (3) limestone exhibited the lowest MSE at 10 kN drilling pressure and 50 r/min rotational speed; and (4) dolomite showed the minimum energy consumption at 10 kN drilling pressure and 25 r/min rotational speed. On this basis, this paper establishes a cutting mechanics model for single-crystal diamond and a working load calculation model for the entire bit, respectively. The cutting mechanics model for single-crystal diamond is re-established based on Hertzian contact theory and elastic-plastic deformation theory. The findings of this study are expected to provide a working load calculation method for diamond coring bits in typical complex and challenging drilling formations and offer technical support for the design of coring bit cutting structures and the development of customized new products. It should be noted that the conclusions of this study are limited to the experimental parameter range (drilling pressure: 5–15 kN; rotational speed: 25–80 r/min), and their applicability under higher load conditions requires further verification. Full article
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27 pages, 4079 KB  
Article
Plastic Strain Spread Study for the Optimal Design of Multistep Flexural Steel Beam Elements
by Salvatore Benfratello and Luigi Palizzolo
Sci 2026, 8(1), 15; https://doi.org/10.3390/sci8010015 - 12 Jan 2026
Viewed by 84
Abstract
The present paper concerns a new formulation of the optimal design problem of I-shaped multistep steel beam elements, based on the study of the plastic strain spread occurring in the relevant elements, with the aim of determining the length involved by the plastic [...] Read more.
The present paper concerns a new formulation of the optimal design problem of I-shaped multistep steel beam elements, based on the study of the plastic strain spread occurring in the relevant elements, with the aim of determining the length involved by the plastic deformation related to assigned load conditions and different constrained beam schemes. Material behavior is assumed as elastic–perfectly plastic, and the hypothesis of plane cross-sections is accepted. The functions defining the plastic strain spread are analytically obtained in the framework of Euler–Bernoulli beam theory. The proposed optimal design problem is a minimum volume one and the new constraint imposed on the length of the plasticized portion ensures that the minimum volume beam element also represents a maximum plastic dissipation one. Furthermore, the solution to the optimal design problem guarantees that the obtained multistep beam element ensures protection against brittle failure of the beam end sections, provides optimal cross-sections of the different portions belonging to Class 1 and ensures a suitable minimum value of the elastic flexural stiffness to respect the constraint on the deflection. Explicit reference is made to the so-called Reduced Beam Section (RBS), which characterizes the described multistep beam elements. Actually, the proposed formulation represents an innovative approach to obtaining an optimal beam element that really satisfies all the resistance, stiffness and ductility behavioral requirements. Some numerical applications conclude the paper, and their results are confirmed by appropriate FEM analyses in ABAQUS environment. Full article
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17 pages, 4208 KB  
Article
Equivalent Elastic Modulus Study of a Novel Quadrangular Star-Shaped Zero Poisson’s Ratio Honeycomb Structure
by Aling Luo, Dong Yan, Zewei Wu, Hong Lu and He Ling
Symmetry 2026, 18(1), 127; https://doi.org/10.3390/sym18010127 - 9 Jan 2026
Viewed by 230
Abstract
This study proposes a novel four-pointed-star-shaped honeycomb structure having zero Poisson’s ratio, designed to overcome the stress concentration inherent in traditional point-to-point connected star-shaped honeycombs.By introducing a horizontal connecting wall at cell junctions, the new configuration achieves a more uniform stress distribution and [...] Read more.
This study proposes a novel four-pointed-star-shaped honeycomb structure having zero Poisson’s ratio, designed to overcome the stress concentration inherent in traditional point-to-point connected star-shaped honeycombs.By introducing a horizontal connecting wall at cell junctions, the new configuration achieves a more uniform stress distribution and enhanced structural stability. An analytical model for the in-plane equivalent elastic modulus was derived using homogenization theory and the energy method. The model, along with the structure’s zero Poisson’s ratio characteristic, was validated through finite element simulations and experimental compression tests. The simulations predicted an equivalent elastic modulus of 51.71 MPa (Y-direction) and 74.67 MPa (X-direction), which aligned closely with the experimental measurements of 56.61 MPa and 60.50 MPa, respectively. The experimental Poisson’s ratio was maintained near zero (v = 0.02). Parametric analysis further revealed that the in-plane equivalent elastic modulus decreases with increases in the wall angle, horizontal wall length, and wall thickness. This work demonstrates a successful structural optimization strategy that improves both mechanical performance and manufacturability for zero Poisson’s ratio honeycomb applications. Full article
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28 pages, 5461 KB  
Article
Free Vibration and Static Behavior of Bio-Inspired Helicoidal Composite Spherical Caps on Elastic Foundations Applying a 3D Finite Element Method
by Amin Kalhori, Mohammad Javad Bayat, Masoud Babaei and Kamran Asemi
Buildings 2026, 16(2), 273; https://doi.org/10.3390/buildings16020273 - 8 Jan 2026
Viewed by 170
Abstract
Spherical caps exploit their intrinsic curvature to achieve efficient stress distribution, delivering exceptional strength-to-weight ratios. This advantage renders them indispensable for aerospace systems, pressurized containers, architectural domes, and structures operating in extreme environments, such as deep-sea or nuclear containment. Their superior load-bearing capacity [...] Read more.
Spherical caps exploit their intrinsic curvature to achieve efficient stress distribution, delivering exceptional strength-to-weight ratios. This advantage renders them indispensable for aerospace systems, pressurized containers, architectural domes, and structures operating in extreme environments, such as deep-sea or nuclear containment. Their superior load-bearing capacity enables diverse applications, including satellite casings and high-pressure vessels. Meticulous optimization of geometric parameters and material selection ensures robustness in demanding scenarios. Given their significance, this study examines the natural frequency and static response of bio-inspired helicoidally laminated carbon fiber–reinforced polymer matrix composite spherical panels surrounded by Winkler elastic foundation support. Utilizing a 3D elasticity approach and the finite element method (FEM), the governing equations of motion are derived via Hamilton’s Principle. The study compares five helicoidal stacking configurations—recursive, exponential, linear, semicircular, and Fibonacci—with traditional laminate designs, including cross-ply, quasi-isotropic, and unidirectional arrangements. Parametric analyses explore the influence of lamination patterns, number of plies, panel thickness, support rigidity, polar angles, and edge constraints on natural frequencies, static deflections, and stress distributions. The analysis reveals that the quasi-isotropic (QI) laminate configuration yields optimal vibrational performance, attaining the highest fundamental frequency. In contrast, the cross-ply (CP) laminate demonstrates marginally best static performance, exhibiting minimal deflection. The unidirectional (UD) laminate consistently shows the poorest performance across both static and dynamic metrics. These investigations reveal stress transfer mechanisms across layers and elucidate vibration and bending behaviors in laminated spherical shells. Crucially, the results underscore the ability of helicoidal arrangements in augmenting mechanical and structural performance in engineering applications. Full article
(This article belongs to the Special Issue Applications of Computational Methods in Structural Engineering)
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22 pages, 1233 KB  
Article
Research on Risk Contagion and Risk Early Warning of China’s Fintech and Banking Industry from the Perspective of Complex Networks
by Peng Sun, Xin Xiang and Kaiyue Ye
Mathematics 2026, 14(2), 220; https://doi.org/10.3390/math14020220 - 6 Jan 2026
Viewed by 224
Abstract
This study selects daily data from 27 fintech companies and 16 listed commercial banks between January 2015 and December 2024 as research samples. Based on complex network theory, we construct an integrated analytical framework encompassing risk measurement, regime identification, and early warning system [...] Read more.
This study selects daily data from 27 fintech companies and 16 listed commercial banks between January 2015 and December 2024 as research samples. Based on complex network theory, we construct an integrated analytical framework encompassing risk measurement, regime identification, and early warning system construction through HD-TVP-VAR model coupled with the Elastic Net algorithm, MS-AR model, and dynamic Logit model. The findings reveal that the total risk spillover rate between fintech and banking ranges from 73.09% to 95.18%, demonstrating significant time-varying and event-driven characteristics in risk contagion. The risk contagion evolution is characterized by three distinct phases: net risk absorption by the banking sector, bidirectional equilibrium contagion, and net risk dominance by the fintech sector. Joint-stock commercial banks and city commercial banks exhibit higher sensitivity to fintech risks compared to state-owned large commercial banks. Key hubs for risk contagion include institutions like Yinxin Technology and Huaxia Bank, with concentrated risk contagion within industry clusters. The MS-AR model accurately delineates low-, medium-, and high-risk zones, showing strong alignment between high-risk periods and major events. The dynamic Logit model incorporating total risk correlation indices demonstrates high consistency between early warning signals and risk evolution trajectories, providing theoretical and practical references for cross-industry systemic financial risk prevention. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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24 pages, 2567 KB  
Article
Theoretical Study on Pipeline Settlement Induced by Excavation of Ultra-Shallow Buried Pilot Tunnels Based on Stochastic Media and Elastic Foundation Beams
by Caijun Liu, Yang Yang, Pu Jiang, Xing Gao, Yupeng Shen and Peng Jing
Appl. Sci. 2026, 16(2), 590; https://doi.org/10.3390/app16020590 - 6 Jan 2026
Viewed by 127
Abstract
Excavation of ultra-shallow pilot tunnels triggers surface settlement and endangers surrounding pipelines. The discontinuous settlement curve from traditional stochastic medium theory cannot be directly integrated into the foundation beam model, limiting pipeline deformation prediction accuracy. The key novelty of this study lies in [...] Read more.
Excavation of ultra-shallow pilot tunnels triggers surface settlement and endangers surrounding pipelines. The discontinuous settlement curve from traditional stochastic medium theory cannot be directly integrated into the foundation beam model, limiting pipeline deformation prediction accuracy. The key novelty of this study lies in proposing an improved coupled method tailored to ultra-shallow burial conditions: converting the discontinuous settlement solution into a continuous analytical one via polynomial fitting, embedding it into the Winkler elastic foundation beam model, and realizing pipeline settlement prediction by solving the deflection curve differential equation with the initial parameter method and boundary conditions. Four core factors affecting pipeline deformation are identified, with pilot tunnel size as the key. Shallower depth (especially 5.5 m) intensifies stratum disturbance; pipeline parameters (diameter, wall thickness, elastic modulus) significantly impact bending moment, while stratum elastic modulus has little effect on settlement. Verified by the Xueyuannanlu Station project of Beijing Rail Transit Line 13, theoretical and measured settlement trends are highly consistent, with core indicators meeting safety requirements (max theoretical/measured settlement: −10.9 mm/−8.6 mm < 30 mm; max rotation angle: −0.066° < 0.340°). Errors (max 5.1 mm) concentrate at the pipeline edge, and conservative theoretical values satisfy engineering safety evaluation demands. Full article
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23 pages, 13894 KB  
Article
Study on the Mechanical Properties and Microscopic Damage Constitutive Equation of Coal–Rock Composites Under Different Strain Rates
by Guang Wen, Peilin Gong, Tong Zhao, Kang Yi, Jingmin Ma, Wei Zhang, Yanhui Zhu, Peng Li and Libin Bai
Appl. Sci. 2026, 16(2), 579; https://doi.org/10.3390/app16020579 - 6 Jan 2026
Viewed by 148
Abstract
Under the influence of engineering disturbances, the loading rate of surrounding rock is in a state of continuous adjustment. This study conducts experimental investigations on the mechanical response characteristics under different strain rates (10−5 s−1, 10−4 s−1, [...] Read more.
Under the influence of engineering disturbances, the loading rate of surrounding rock is in a state of continuous adjustment. This study conducts experimental investigations on the mechanical response characteristics under different strain rates (10−5 s−1, 10−4 s−1, and 10−3 s−1). During the uniaxial loading process of coal–rock composite specimens, multi-parameter monitoring was implemented, and a systematic study was carried out on the ring-down count induced by microcracks, the energy values of acoustic emission (AE) events, the stage-dependent strain characteristics on the specimen surface, and the surface temperature variation characteristics. Additionally, the stress–strain curve characteristics under different strain rates were comparatively analyzed in stages. The loading process of the coal–rock composite specimens was reproduced using the Particle Flow Code (PFC3D 6.0) simulation software. The simulation results indicate that the stress–strain results obtained from the simulation are in good agreement with the laboratory test results; based on these simulation results, the energy accumulation and dissipation characteristics of the coal–rock composite specimens under the influence of strain rate were revealed. Furthermore, a microscopic damage model considering strain rate was constructed based on the Weibull probability statistics theory. The results show that strain rate has a significant impact on the strength, elastic modulus, and failure mode of the coal–rock composite specimens. At low strain rates, the specimens exhibit obvious progressive failure characteristics and strain localization phenomena, while at higher strain rates, they show brittle sudden failure characteristics. Meanwhile, the thermal imaging results reveal that at high strain rates, the overall temperature rise in the composite specimens is rapid, whereas at low strain rates, the overall temperature rise is slow—but the temperature rise in the coal portion is faster than that in the rock portion. The peak temperature at high strain rates is approximately 2 °C higher than that at low strain rates. The PFC simulation results demonstrate that the larger the strain rate, the faster the growth rate of plastic energy in the post-peak stage and the faster the release rate of elastic energy. Full article
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42 pages, 1106 KB  
Article
Nonlinear Transport of Tracer Particles Immersed in a Strongly Sheared Dilute Gas with Inelastic Collisions
by David González Méndez and Vicente Garzó
Mathematics 2026, 14(1), 179; https://doi.org/10.3390/math14010179 - 3 Jan 2026
Viewed by 147
Abstract
Nonlinear transport of tracer particles immersed in a sheared dilute gas with inelastic collisions is analyzed within the framework of the Boltzmann kinetic equation. Two different yet complementary approaches are employed to obtain exact results. First, we maintain the structure of the inelastic [...] Read more.
Nonlinear transport of tracer particles immersed in a sheared dilute gas with inelastic collisions is analyzed within the framework of the Boltzmann kinetic equation. Two different yet complementary approaches are employed to obtain exact results. First, we maintain the structure of the inelastic Boltzmann collision operator but consider inelastic Maxwell models (IMMs) instead of the realistic model of inelastic hard spheres (IHS). Using IMMs enables us to compute the collisional moments of the inelastic Boltzmann operator for mixtures without explicitly knowing the velocity distribution functions of the mixture. Second, we consider a kinetic model of the Boltzmann equation for IHS. This kinetic model is based on the equivalence between a gas of elastic hard spheres subjected to a drag force proportional to the particle velocity and a gas of IHS. We solve the Boltzmann–Lorentz kinetic equation for tracer particles using a generalized Chapman–Enskog-like expansion around the shear flow distribution. This reference distribution retains all hydrodynamic orders in the shear rate. The mass flux is obtained to first order in the deviations of the concentration, pressure, and temperature from their values in the reference state. Due to the anisotropy induced in the velocity space by shear flow, the mass flux is expressed in terms of tensorial quantities rather than conventional scalar diffusion coefficients. Unlike the previous results obtained for IHS using different approximations, the results derived in this paper are exact. Generally, the comparison between the IHS results and those found here shows reasonable quantitative agreement, especially for IMM results. This good agreement shows again evidence of the reliability of IMMs for studying rapid granular flows. Finally, we analyze segregation by thermal diffusion as an application of the theory. Phase diagrams illustrating segregation are presented and compared with previous IHS results, demonstrating qualitative agreement. Full article
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12 pages, 2502 KB  
Article
A First-Principles Study of Lithium Adsorption and Diffusion on Graphene and Defective-Graphene as Anodes of Li-Ion Batteries
by Lina Si, Yijian Yang, Yuhao Wang, Qifeng Wu, Rong Huang, Hongjuan Yan, Mulan Mu, Fengbin Liu and Shuting Zhang
Coatings 2026, 16(1), 52; https://doi.org/10.3390/coatings16010052 - 3 Jan 2026
Viewed by 264
Abstract
Defective graphene has emerged as a promising strategy to enhance electrochemical performance of pristine graphene (p-Gr) as anodes in lithium-ion batteries (LIBs). Herein, we perform a comprehensive first-principles study based on density functional theory (DFT) to systematically investigate the Li adsorption, charge transfer, [...] Read more.
Defective graphene has emerged as a promising strategy to enhance electrochemical performance of pristine graphene (p-Gr) as anodes in lithium-ion batteries (LIBs). Herein, we perform a comprehensive first-principles study based on density functional theory (DFT) to systematically investigate the Li adsorption, charge transfer, and diffusion behaviors of p-Gr and defective graphene (d-Gr) with single vacancy (SV Gr) and double vacancy (DV5-8-5 Gr) defects, aiming to clarify the mechanism by which defects modulate Li storage performance. Structural optimization reveals that SV Gr undergoes notable out-of-plane distortion after Li adsorption, while DV5-8-5 Gr retains planar geometry but exhibits more significant C-C bond length variations compared to p-Gr. Binding energy results confirm that defects enhance Li adsorption stability, with DV5-8-5 Gr showing the strongest Li–graphene interaction, followed by SV Gr and p-Gr. Bader charge analysis and charge density difference plots further validate that defects enhance charge transfer from Li ions to graphene. Using the nudged elastic band (NEB) method, we find that defects reduce Li diffusion barriers: DV5-8-5 Gr exhibits a lower barrier than p-Gr. Our findings demonstrate that DV5-8-5 Gr exhibits the most favorable Li storage performance, providing a robust theoretical basis for designing high-performance graphene anodes for next-generation LIBs. Full article
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21 pages, 3366 KB  
Article
A Theory for Plane Strain Tangential Contacts of Functionally Graded Elastic Solids with Application to Fretting
by Markus Heß, Paul Leonard Giesa, Larissa Riechert and Josefine Wilhayn
Appl. Sci. 2026, 16(1), 473; https://doi.org/10.3390/app16010473 - 2 Jan 2026
Viewed by 263
Abstract
Due to their superior tribological properties compared to conventional materials, the use of functionally graded materials (FGMs) has long become indispensable in mechanical engineering. The wide variety of in-depth gradings means that solving contact problems requires specific, complex numerical analysis. In many cases, [...] Read more.
Due to their superior tribological properties compared to conventional materials, the use of functionally graded materials (FGMs) has long become indispensable in mechanical engineering. The wide variety of in-depth gradings means that solving contact problems requires specific, complex numerical analysis. In many cases, however, the spatial change in Young’s modulus can be approximated by a power law, which allows closed-form analytical solutions. In the present work, integral equations for solving tangentially loaded power-law graded elastic half-planes are derived by using the Mossakovskii–Jäger procedure. In this way, the application of highly complicated singular integrals arising from a superposition of fundamental solutions is avoided. A distinction is made between different mixed boundary conditions. The easy tractability of the novel equations is substantiated by solving the plane strain fretting contact of a rigid parabolic cylinder and a power-law graded (PLG) elastic half-space. The effect of the type of in-depth grading on the dissipated energy density and the total energy lost per cycle is investigated in detail. A comparison of the total dissipated energy per cycle shows that, for very thin stiff layers on soft substrates, the total dissipated energy exceeds that of a homogeneous material. The same trend is observed for thick layers of a functionally graded material whose Young’s modulus gradually increases with depth, matching that of the underlying substrate at the bonded interface. In addition, a closed-form analytical solution for the total dissipated energy per cycle for plane strain parabolic contact of elastically homogeneous material is presented for the first time. Full article
(This article belongs to the Section Mechanical Engineering)
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