Search Results (999)

High-water material (HWM) is widely used for roadside filling in gob-side entry retaining (GER), where its creep behavior under sustained loading critically influences the long-term stability of the roadway. To enhance the long-term mechanical performance of HWM, this study modified it with polyethylene (PE) fiber and conducted uniaxial compression creep tests to investigate the effects of fiber content on time-dependent deformation, long-term strength, and failure time. The results indicate that when the applied stress remains below the long-term strength, the creep deformation of PE fiber-modified HWM stabilizes over time. In contrast, under higher stress levels, the deformation of HWM continuously develops over time and progresses through three stages: attenuation, steady-state, and accelerated creep, ultimately resulting in failure. Compared with pure HWM, the fiber-modified material exhibits a significant improvement in long-term strength, which increases linearly with fiber content. Furthermore, a higher fiber content raises the stress threshold for creep failure and substantially extends the time to failure. To predict the creep response of PE fiber-modified HWM, a viscoelastic-plastic creep damage model was developed using the component combination method, incorporating the Riemann–Liouville fractional-order integral operator and a time-dependent damage evolution equation. The reliability of the model was verified by utilizing the experimental data, and a sensitivity analysis of the model parameters was carried out based on the fitting results. The proposed model can not only describe the creep behavior of HWM across all loading stages, including the accelerated creep phase, but also accounts for the effect of fiber content on long-term strength. These findings can provide a theoretical foundation for the design and stability assessment of fiber-reinforced HWM roadside backfills in GER engineering. Full article

This Editorial introduces the Symmetry Special Issue “Theory and Applications of Special Functions II” and summarizes the nine contributions collected therein. The papers span the analytic continuation of multivariate hypergeometric functions; stability theory for differential equations via integral transforms; numerical schemes for multi-space fractional partial differential equations based on nonstandard finite differences and orthogonal polynomials; applications of the Lambert W function to viscoelastic creep modeling; algebraic constructions of new Hermite-type polynomial families via the monomiality principle; higher-level generalizations of poly-Cauchy numbers; Bell-polynomial expansions for Laplace transforms of higher-order nested functions; and two complementary studies on the physical implementation and algebraic description of Gaussian quantum states. Beyond the contributions of the Special Issue, we highlight methodological connections—continued fractions and complex analysis, transform techniques, special polynomials, and combinatorial sequences—and emphasize the unifying role of symmetry across mathematical structures and applications. Full article

The multi-objective optimization of multicomponent superalloys has long been impeded by not only the complex interactions among multiple elements but also the low efficiency and high cost of traditional trial-and-error methods. To address this issue, this study proposed a thermodynamic calculation data-driven optimization framework that integrates machine learning (ML) and multi-objective screening based on domain knowledge. The core of this methodology involves introducing a commercial reference alloy and rapidly generating a large-scale thermodynamic dataset through ML models. After training, the ML models were verified to be more efficient at predicting phase transition temperatures and γ′ volume fractions than the CALPHAD methods. Focusing on the mechanical properties, critical strength indices, including solid solution strengthening, precipitation strengthening, and creep resistance based on the calculated γ/γ′ two-phase compositions, were compared with the reference alloy and set as the critical screen criteria. Optimal alloys were selected from the 388,000 candidates. Compared with the reference alloy, two new alloys were experimentally verified to have superior or comparable compressive yield strength and creep resistance at 900 °C at the expense of oxidation resistance and density, while maintaining comparable cost. This work demonstrates the significant potential of combining high-throughput thermodynamic data with intelligent multi-objective optimization to accelerate the development of new alloys with tailored property profiles. Full article

Creeping landslides constitute the predominant form of long-term, slow-moving geohazards in high mountain gorge regions. Under the combined influence of gravity and external triggering factors, these landslides undergo persistent deformation, posing continuous threats to major transportation corridors, hydropower infrastructures, and nearby settlements. Li County is located within the active tectonic belt along the eastern margin of the Tibetan Plateau, characterized by highly variable topography, intensely fractured rock masses, and dense development of creeping landslides. The slip surfaces are typically deeply buried and concealed. Consequently, conventional drilling and profile-based investigations, limited by high costs, sparse sampling points, and poor spatial continuity, are insufficient for identifying the deep-seated structures of such landslides. To address this challenge, this study applies Small Baseline Subset Interferometric Synthetic Aperture Radar (SBAS-InSAR) to obtain ascending and descending deformation rate fields for 2022–2024, revealing pronounced spatial heterogeneity and persistent activity across three types of landslides. Based on the principle of mass conservation, the sliding-surface depths of eight typical landslides were inverted, revealing pronounced heterogeneity. The maximum sliding-surface depths range from 32 to 98 m and show strong agreement with borehole and profile data (R² > 0.92; RMSE ±4.96–±16.56 m), confirming the reliability of the inversion method. The GeoDetector model was used to quantitatively evaluate the dominant factors controlling landslide depth. Elevation was identified as the primary control factor, while slope aspect exhibited significant influence in several landslides. All factor combinations showed either “bi-factor enhancement” or “nonlinear enhancement”, indicating that slip-surface depth is governed by synergistic interactions among multiple factors. Boxplot-based statistical analyses further revealed three typical patterns of slip-surface variation with elevation and slope, based on which the landslides were classified into rotational, push-type translational, and traction-type translational categories. By integrating statistical patterns with mechanical models, the study achieves a transition from “form” to “state”, enabling inference of the internal mechanical conditions and evolutionary stages from the observed surface morphology. The results of this study provide an effective technical approach for deep structural detection, identification of controlling factors, and stability evaluation of creeping landslides in high mountain gorge environments. Full article

This paper presents an analytical model for the hereditary vibrations of a coupled circular plate system interconnected by viscoelastic creep layers. The system is represented as a discrete-continuous chain of thin, isotropic plates with time-dependent material properties. Based on the theory of hereditary viscoelasticity and D’Alembert’s principle, a system of partial integro-differential equations is derived and reduced to ordinary integro-differential equations using Bernoulli’s method and Laplace transforms. Analytical expressions for natural frequencies, mode shapes, and time-dependent response functions are obtained. The results reveal the emergence of multi-frequency vibration regimes, with modal families remaining temporally uncoupled. This enables the identification of resonance conditions and dynamic absorption phenomena. The fractional parameter serves as a tunable damping factor: lower values result in prolonged oscillations, while higher values cause rapid decay. Increasing the kinetic stiffness of the coupling layers raises vibration frequencies and enhances sensitivity to hereditary effects. This interplay provides deeper insight into dynamic behavior control. The model is applicable to multilayered structures in aerospace, civil engineering, and microsystems, where long-term loading and time-dependent material behavior are critical. The proposed framework offers a powerful tool for designing systems with tailored dynamic responses and improved stability. Full article

As key driving and supporting components of spacecraft, pod-type space self-deployable structures have terminal pointing accuracy that directly affects overall spacecraft performance. To clarify the influence of the structure’s machining deformation on its pointing accuracy, this study focuses on two key processes, namely laser welding and hot forming. Based on the bionic symmetric structural characteristics of pod-type structures, a laser welding finite element model with a surface Gaussian heat source and a hot forming constitutive model coupled with creep aging were established. An orthogonal experimental design was adopted: for laser welding, three parameters, namely laser power, spot diameter, and welding speed, each with three levels, were selected, and an L₉(3³) orthogonal table was constructed to conduct nine groups of simulations; for hot forming, two parameters, namely processing temperature and holding time, each with three levels, were chosen, and nine groups of simulations were designed based on the first two columns of the L₉(3⁴) orthogonal table. The combined method of residual analysis and analysis of variance was used to quantitatively identify the influence of each process parameter on pointing accuracy. The results show that in laser welding, welding speed has the most significant impact on deformation, followed by laser power, and spot diameter has the least; in hot forming, processing temperature and holding time have similar effects on deformation. Physical machining verification was performed, and the actually measured deformations are 0.164 mm and 0.034 mm, which are close to the simulation results of 0.176 mm and 0.047 mm, meeting the index requirement that the terminal pointing deformation of a single pod structure is less than 0.2 mm. The results can provide a theoretical basis and engineering reference for the actual machining of such structures. Full article

The viscoelastic properties of ultraviolet radiation-curable polymer coatings of optical fibers were studied experimentally and numerically. The test setup was completed, and a series of natural experiments were conducted for an extended temperature range from −110 °C to +120 °C using a dynamic mechanical analyzer (DMA). Discrete dependencies of the complex modulus on temperature and frequency of kinematic loading were obtained. The problem of multiparametric optimization was solved. Defining relations were obtained for protective coating polymers, making it possible to describe the thermomechanical behavior of the glass-forming materials under consideration in a wide temperature range, including relaxation transition. The optimal solution was found for 18 series terms at the selected reference temperature T_r = −70 °C, C₁ = 20.036, and C₂ = 32.666 for the DeSolite 3471-1-152A material. The optimal solution was found for 60 series terms at the selected reference temperature T_r = 0 °C, C₁ = 40,242.2827, and C₂ = 267,448.888 for the DeSolite DS-2015 material. The models were verified according to the data of creep experiments. The capabilities of the viscoelastic model were demonstrated by the example of a numerical experiment on free thermal heating/cooling of a Panda-type optical fiber. Full article

Diffusion-controlled processes play a critical role in the heat treatment and microstructural homogenization of β-titanium alloys containing multiple β-stabilizing elements. Adding β-phase stabilizing elements like Cr and Nb to titanium alloys can significantly improve the high-temperature strength and creep performance of the alloy. Their diffusion coefficients can be used to predict the risk of softening and creep failure in high-temperature components caused by diffusion. However, reliable diffusion kinetic data for the β phase in the Ti–Cr–Nb ternary system remain scarce, limiting quantitative process modeling and simulation. In this study, diffusion behavior in the BCC (β) region of the Ti–Cr–Nb system was investigated using diffusion couples combined with CALPHAD-based kinetic modeling. Twelve sets of diffusion couples were prepared and annealed at 1373 K for 48 h, 1423 K for 36 h, and 1473 K for 24 h. The corresponding composition–distance profiles were measured by electron probe microanalysis. Composition-dependent interdiffusion coefficients and atomic mobility parameters were determined using the numerical inverse method. The results revealed temperature and composition dependence of the main interdiffusion coefficients, with Nb exhibiting a stronger influence than Cr. The evaluated kinetic parameters provide an effective kinetic description for diffusion-controlled process simulations. Full article

Structural adhesives in aeronautical applications are routinely exposed to complex loading histories that generate time-dependent deformation, making accurate prediction of their viscoelastic response essential for reliable assessment of joint integrity. This work presents an integrated experimental and modeling study of the aerospace-grade epoxy adhesive 3M Scotch-Weld EC-2216 using multi-step creep and stress-relaxation tests performed at room temperature and controlled loading rates, combined with fractional viscoelastic modeling. Unlike traditional single-step characterizations, the multi-step protocol employed here captures the cumulative loading effects and fading-memory dynamics that govern the adhesive’s mechanical response. The experimental data were analyzed using fractional Maxwell, Voigt–Kelvin, and Zener formulations. Statistical evaluation based on the Bayesian Information Criterion (BIC) consistently identified the Fractional Zener Model (FZM) as the most robust representation of the stress-relaxation behavior, effectively capturing both the unrelaxed and relaxed modulus. The results demonstrate that EC-2216 exhibits hierarchical relaxation mechanisms and history-dependent viscoelasticity that cannot be accurately described by classical integer-order models. Overall, the study validates the use of fractional operators to represent the broad and hierarchical relaxation spectra typical of toughened aerospace epoxies and provides a rigorous framework for durability assessment and predictive modeling of adhesively bonded structures. Full article

With unconventional oil–gas reservoir exploration and oil and gas theory development, more and more importance is attached to the wellbore integrity. The casing deformation and damage is an integral part of the wellbore integrity theory. In the shale gas block in southwestern China, the casing deformation is grave because of the nonuniform stress of the reservoir, posing a significant influence on the productivity and economic efficiency of the shale gas development. In order to clarify the causes and mechanisms of the casing deformation caused by the nonuniform stress, the author of this paper has established the mechanical properties mathematical model of the casing under the nonuniform load as well as the casing–cement ring–stratum assembly numerical model based on the data of in situ multi-arm well logger and reservoir geological characteristics. Such models are established to study the response pattern of the casing under the nonuniform creep ground stress of the shale gas reservoir. The study herein serves as a reference for the optimization of casing design and target-specific exploration technology adjustments and lays the foundation for promoting the cost-effective development of shale gas reservoirs. Full article

With the advancement in deep-sea resource development, the creep behavior of deep-sea remolded sediments under coupled temperature, confining pressure (σ₃), and stress effects has become a critical issue threatening engineering stability. The traditional Singh–Mitchell model, limited by its neglect of temperature effects and prediction of infinite strain, struggles to meet deep-sea environmental requirements. Based on low-temperature, high-pressure triaxial tests (with temperatures ranging from 4 to 40 °C and confining pressures ranging from 100 to 300 kPa), this study proposes a modified model incorporating temperature–stress–time coupling. The model introduces a hyperbolic creep strain rate decay function to achieve strain convergence, establishes a saturated strain–stress exponential relationship, and quantifies the effect of temperature on characteristic time via coupling through the Arrhenius equation. The modified model demonstrates R² values > 0.96 for full-condition creep curves. The results show several key findings: a 10 °C increase in temperature leads to a 30–50% growth in the steady-state creep rate; a 100 kPa increase in confining pressure enhances long-term strength by 20–30%. 20 °C serves as a critical temperature point. At this point, strain amplification reaches 2.1 times that of low-temperature ranges. These experimental findings provide crucial theoretical foundations and technical support for incorporating soil creep effects in deep-sea engineering design. Full article

Thermal and nuclear power systems require materials capable of sustaining high mechanical and thermal loads over prolonged service durations. Among these, 9Cr heat-resistant steels are particularly attractive due to their superior mechanical strength and extended creep rupture life, making them suitable for extreme environments. In this study, multiple machine learning models were explored to predict the creep rupture life of 9Cr heat-resistant steels. A comprehensive dataset of 913 samples, compiled from experimental results and literature, included eight input variables—covering chemical composition, stress, and temperature—and one output variable, the creep rupture life. The optimized artificial neural network (ANN) model achieved the highest predictive accuracy with a regularization coefficient of 0.01, 10,000 training iterations, and five hidden layers with 30 neurons per layer, attaining an R² of 0.9718 for the test dataset. Beyond accurate prediction, single- and two-variable sensitivity analyses were used to elucidate statistically meaningful trends and interactions among the input parameters governing creep rupture life. The analyses indicated that among all variables, test conditions—particularly the test temperature—exert a pronounced negative effect on creep life, significantly reducing durability at elevated temperatures. Additionally, an optimization module enables identification of input conditions to achieve desired creep life, while the Index of Relative Importance (I_RI) and quantitative effect analysis enhance interpretability. This framework represents a robust and reliable tool for long-term creep life assessment and the design of 9Cr steels for high-temperature applications. Full article

Bitumen content is a critical factor influencing the long-term performance and durability of asphalt pavements. This study evaluates how different binder percentages affect the mechanical behaviour of asphalt mixtures. Mixtures containing 4.7%, 5.1% and 5.5% binder were tested through an extensive experimental program that included Marshall stability and flow, semi-circular bending, PAV aging, wheel rutting, dynamic modulus, creep compliance and fatigue resistance, supported by finite element simulations. To model the nonlinear viscoplastic and damage behaviour, a Perzyna-type viscoplastic formulation and Lemaitre’s isotropic damage model were applied. Model parameters were further refined using Bayesian estimation, based on 10,000 samples generated with a Markov Chain Monte Carlo procedure employing the Metropolis–Hastings algorithm. The findings indicate that mixtures with 4.7% binder content develop fatigue damage earlier, while increasing the binder above 5.1% leads to greater rutting susceptibility and higher creep compliance, as seen in the 5.5% mixture. Among the three, the 5.1% binder content delivered the best overall performance, reducing plastic strain-related damage by 40% compared with the 4.7% mixture and by 27% compared with the 5.5% mixture. Full article

To enhance construction efficiency and structural stability, this study investigates the mechanical behavior and deformation characteristics of a jacking steel platform system used in the core-tube construction of a supertall building. Field monitoring was conducted on site to record stress, settlement, and inclination during the jacking, construction, and self-climbing stages. A finite element model was developed to simulate the platform’s mechanical response and validated against the field measurements. Results indicate that stress and deformation remained within safe limits throughout all stages, and the vertical deformation difference between the core tube and the outer frame was primarily governed by concrete shrinkage and creep. An improved modular design was proposed to address connection limitations in the steel truss, and cross-section optimization was applied using the stress ratio method. Comparative analysis against the original diamond-type truss baseline showed that the improved system increased overall strength by 5.88% and stiffness by 4.82% while enhancing truss versatility and structural stability. These findings provide a technical basis for the modular design and optimization of jacking steel platform systems, contributing to safer and more efficient construction practices. Full article

Alfalfa is a high-quality forage crop whose viscoelastic properties strongly influence the performance of baling, pickup, and stacking operations. In this study, small alfalfa block specimens were tested using a universal testing machine to investigate stress relaxation and creep behaviors under different moisture contents (12%, 15%, 18%), densities (100, 150, 200 kg/m³), and maximum compressive stresses (8, 12, 16 kPa). Experimental data were fitted using viscoelastic models for parameter analysis. Results indicated that the relaxation response consisted of a rapid attenuation followed by a slow stabilization phase. The five-element Maxwell model achieved a higher fitting accuracy (coefficient of determination, R² > 0.997) than the three-element model. The creep process exhibited three stages, including instantaneous elastic deformation, decelerated creep, and steady-state deformation, and it was accurately represented by the five-element Kelvin model (R² > 0.998). Increasing moisture content reduced stiffness, while moderate moisture improved viscosity and shape retention. Higher density enhanced blocks compactness, stiffness, and damping characteristics, resulting in smaller deformation. The viscoelastic response to compressive stress showed moderate enhancement followed by attenuation under overload, with the best recovery and deformation resistance observed at 12 kPa. These findings elucidate the viscoelastic behavior of alfalfa blocks and provide theoretical support and engineering guidance for evaluating bale stability and optimizing pickup–clamping parameters. Full article