Abstract: Since the era of Newton and Leibniz, the concept of the material element in continuum mechanics has played a fundamental role. When the research perspective expands from traditional engineering materials to living organisms, the classic concept of the material element faces new challenges due to the multi-scale and multi-level characteristics of living organisms. This article focuses on the intersection of fractals and fractional calculus, analyzes the abstraction process of fractal snowflakes and physical fractal spaces from biological multi-level structures, and reviews the exploration process of fractional-order mechanics. This article starts from two classic problems, namely the "Mandelbrot Question" and the "L’Hospital Question", and presents the following exploration paths: (a) from geometric fractals to physical fractals, (b) from kinematics to dynamics, and (c) from fractal dimension to fractional order. The specific content includes: (a) fractal snowflakes abstracted from living organisms and their growth kinematics, (b) fractional-order operators abstracted from living organisms and their theoretical construction; (c) applications of fractional-order operator theory. On this basis, this article delineates the evolutionary trajectory of the material element concept: from the classical element, the representative volume element (RVE), the lattice unit cell, and the mechanical metamaterial unit cell to the fractal cell, and discusses the multiple origins of fractional orders and the spatiotemporal correlation between fractals and fractional calculus. This article concludes that mechanics in the physical fractal spaces exhibits features that are non-integer-order, non-rational, non-elementary, and non-local, offering novel perspectives for broadening the boundaries of mechanics.
Jian Z M, Wang B, Li Q Y, Jiang Z Z, Zhou T Y, Jiang R H, Xin J Q, Yin Y J. From geometric fractals to physical fractals: Concepts, models, and methods of fractional-order mechanics. AdvancesinMechanics, in press. doi: 10.6052/1000-0992-26-035.
Abstract: As protection targets expand from large-scale fixed infrastructure to multi-domain mobile equipment and intelligent unmanned platforms, protective design against intense dynamic loading increasingly requires not only safety assurance under extreme loads but also enhanced effectiveness under resource constraints and improved efficiency in complex loading environments. Based on protection requirements, design philosophies, and representative strategies, three protective modes are identified. The first mode, represented by critical infrastructure, emphasizes robust hardening. It integrates protective capabilities by increasing the degree of structural static indeterminacy and toughening vulnerable components, thereby maintaining overall safety and critical functions. The second mode, primarily targeting multi-domain mobile equipment, emphasizes efficient resource utilization. It achieves performance gains through lightweight configurations by exploiting wave–configuration interactions and coordinated redistribution of momentum and energy. The third mode, focused on intelligent unmanned platforms and precision functional equipment, emphasizes load-specific adaptation. It enables targeted optimization of structural properties and dynamic responses according to the time-domain, frequency-domain, and spatial characteristics of loading. The three modes represent a progression from protection assurance to effectiveness enhancement and efficiency optimization, while remaining complementary in practice. Their common mechanical basis lies in controlling load propagation, energy conversion, structural response, and damage evolution. In engineering applications, the first mode establishes a safety baseline, the second reduces the resources required to achieve it, and the third provides additional benefits through adaptation to specific threats. By clarifying the shared mechanical principles of these modes and their combined application under different protection requirements and operational constraints, this review provides a basis for advancing protective design from experience-driven to mechanics-based approaches and from fixed configurations to intelligent regulation.
Zhang W M, Liu R C, Ren H Q, Ma L, Xu X Y, Ma J, Wang W J. Protective modes for intense dynamic loading and their mechanics-based design. AdvancesinMechanics, in press. doi: 10.6052/1000-0992-26-036.
Abstract: With the increasingly prominent challenges of energy shortages and environmental issues, the development of clean and renewable energy has become a global consensus. Owing to their abundant reserves and renewable nature, wind and water energy are regarded as promising sources for energy harvesting. Mechano-electric coupling mechanisms determine the output power and bandwidth adaptability of energy harvesters and therefore provide an important approach to improving energy harvesting efficiency. This review summarizes recent advances in the application of mechano-electric coupling effects to wind and water energy harvesting, with particular emphasis on energy capture mechanisms based on dynamic instabilities, theoretical modeling methods, and performance enhancement strategies. For wind energy harvesting, typical flow-induced vibration phenomena, including vortex-induced vibration, flutter, and galloping, are discussed with a focus on their nonlinear dynamic response characteristics. Recent progress in broadening the effective operating bandwidth and improving electromechanical conversion efficiency through structural configuration optimization, the introduction of nonlinear mechanisms, and multi-degree-of-freedom coupling designs is also reviewed. For water energy harvesting, linear resonance responses and nonlinear frequency-up-conversion techniques used in macroscopic wave energy harvesting are summarized in terms of their effectiveness in improving energy conversion efficiency, and the micro- and nanoscale mechanical characteristics involved in microscale liquid-water energy harvesting are discussed. Finally, future trends in mechanics-based design for energy harvesting technologies are outlined.
Gao L X, Wang Y H, Xie K, Deng Q B, Tang H, Hu N. Mechano-electric coupling effects in wind and water energy harvesting: Applications and advances. AdvancesinMechanics, in press. doi: 10.6052/1000-0992-26-022.
Abstract: As a transitional region between aeronautics and astronautics, near space is characterized by extreme environmental conditions, including rarefied atmosphere, pronounced thermal stratification, and strong wind-field disturbances. These conditions induce complex coupled effects on the aerodynamics, propulsion, control, materials, and structures of flight vehicles. From the overarching perspective of environment–vehicle coupling effects, this paper systematically reviews the mean atmospheric characteristics and spatiotemporal evolution of the near-space environment, and analyzes the transmission pathways through which environmental parameters affect the subsystems of near-space flight vehicles, as well as the resulting constraints on the flight envelope. In terms of aerodynamics, key issues are discussed, including rarefied-gas effects, wind-field disturbances, aerodynamic heating, thermochemical nonequilibrium, boundary-layer transition, and turbulence simulation. For propulsion systems, this paper reviews the environmental adaptability and major challenges associated with ramjet and scramjet engines, combined-cycle engines, detonation engines, and electric propulsion technologies. With respect to flight dynamics and control, the current state and future trends are analyzed for cross-domain and wide-speed-range guidance strategies, robust control methods under strong disturbances, and intelligent control and autonomous decision-making. Regarding materials and structures, the paper summarizes research progress and future prospects in thermal protection systems, active thermal management, noise and vibration suppression, structural health monitoring, and digital-twin applications under extreme coupled thermal–mechanical–acoustic multi-field environments. Finally, perspectives and several research recommendations are proposed across the above areas. Unlike existing reviews that focus on a single discipline or a specific effect, this paper provides an analytical reference framework and key technological directions for the overall and subsystem-level research of near-space flight vehicles. This framework facilitates the evolution of relevant fields from empirical design to refined and integrated design that adapts to environmental uncertainties, thereby providing support for the future development of near-space flight vehicles.
Teng H H, Ren J, Zhou X M, Han H W, Liu L, Zhang Z J, Huang J S, Zhao R, Miao L, Luo K, Zuo L, Wang D W, Liu Z W. Effects of the near-space environment on flight vehicles: Progress and perspectives. AdvancesinMechanics, in press. doi: 10.6052/1000-0992-26-020.
Abstract: Micro- and nanoscale gas–liquid and liquid–liquid interfaces are ubiquitous in natural and engineering systems, where their physicomechanical behaviors differ significantly from those of macroscopic systems due to pronounced scale effects. Nanobubbles and nanodroplets represent typical soft-matter interfacial systems that can maintain long-term stability under extremely high Laplace pressures, leading to long-standing stability paradoxes. For nanobubbles, their persistent existence deviates significantly from the classical predictions of the Epstein–Plesset diffusion model, whereas nanodroplets exhibit nonequilibrium stabilization beyond the applicability of Ostwald ripening theory. Within the frameworks of continuum mechanics and thermodynamics, this review systematically summarizes the stability mechanisms and evolutionary behaviors of surface nanobubbles, bulk nanobubbles, and nanodroplets. The roles of contact-line pinning and interfacial gas supersaturation in regulating gas diffusion from surface nanobubbles are discussed, together with the stabilization mechanisms of bulk nanobubbles arising from interfacial charge accumulation, ion-specific adsorption, and diffusion shielding. The responses of nanobubble systems to variations in solution conditions and mechanical perturbations are further reviewed. In addition, the nucleation dynamics of nanodroplets in multicomponent solutions and the entropy-driven metastable stabilization mechanisms of surfactant-free microemulsions are discussed. Finally, by comparing curvature effects, interfacial tension corrections, and molecular arrangements at interfaces, a unified physicomechanical framework connecting nanobubbles and nanodroplets is established. Perspectives on multiscale modeling, in situ characterization techniques, and applications in energy and environmental fields are also provided.
Ma X T, Li M B, Gao Y W, Chen C S, Sun C. Interfacial stability mechanisms at the micro- and nanoscale: From nanobubbles to nanodroplets. AdvancesinMechanics, in press. doi: 10.6052/1000-0992-26-024.
Abstract: Vibration-induced structural fatigue, dynamic instability, and functional degradation can significantly reduce the service reliability of engineering equipment, making effective vibration isolation essential. However, conventional linear vibration isolation structures are limited by the inherent trade-off between low static stiffness and load-bearing capacity, which restricts their performance at low frequencies. Quasi-zero-stiffness (QZS) vibration isolation structures have therefore attracted increasing attention because they combine high static stiffness with low dynamic stiffness, enabling vibration isolation at low and even ultra-low frequencies. This paper reviews typical QZS designs, including oblique-spring, linkage–spring, cam–roller, buckled beam/plate/ring, permanent-magnet, origami-inspired, and bio-inspired configurations. Recent developments in multilayer and multidirectional QZS vibration isolation structures are also summarized, together with representative applications in transportation, mechanical transmission, medical equipment, civil engineering, and fluid-conveying pipelines. Finally, future research directions are discussed, including topology optimization, data-driven modelling, active control, and vibration energy harvesting. This review aims to provide a useful reference for further development of QZS vibration isolation technology.
Wang Q, Zhou J X, Wang K, Qin Y, Gao J H, Tan D G. Design and application of quasi-zero-stiffness vibration isolation structures. AdvancesinMechanics, in press. doi: 10.6052/1000-0992-26-028.
Abstract: Marine composite pipes and cables are critical connection structures in offshore energy development. They are typically composed of metallic reinforcement layers, polymer sheaths, functional units, and interfacial layers, and are characterized by multilayer composite configurations, heterogeneous material combinations, and slender flexible geometries. Under the combined effects of complex marine environments and loading conditions, including waves and currents, internal pressure, temperature, floater motions, and seabed constraints, these structures exhibit pronounced material nonlinearity, geometric nonlinearity, interfacial nonlinearity, and contact nonlinearity, which directly affect their structural analysis, strength assessment, and service safety. Focusing on the research progress on nonlinear problems in marine composite pipes and cables, this paper systematically introduces their multilayer composite structural characteristics and the underlying causes of nonlinearity. It reviews the constitutive theories associated with material nonlinearity, including the hyperelastic and viscoelastic behavior of rubber and polymer materials, as well as the elastoplastic constitutive models of metallic materials. The major modeling approaches for geometric nonlinearity, including slender-rod theory, the lumped-mass method, the co-rotational method, and the absolute nodal coordinate formulation, together with the corresponding solution strategies, are comparatively reviewed. The theoretical developments related to interfacial nonlinearity, including interfacial strength, interfacial friction, and interfacial fatigue nonlinearity, are summarized. In addition, the classical theories and improved models for pipe/cable–seabed interaction in contact nonlinearity are discussed. Although substantial progress has been made in existing studies, the understanding of the coupled mechanisms of multiple nonlinearities under complex marine environments remains insufficient. Future research should therefore focus on coupled analyses of multiple nonlinear behaviors under multiphysics, multiscale, and long-term service conditions, so as to provide more reliable theoretical support for the safe design and long-term integrity assessment of marine composite pipes and cables.
Li L J, Lu Z H, Cao T, Liu D P, Zhang Y. Research Progress on Nonlinear Problems of Marine Composite Pipe and Cable. AdvancesinMechanics, in press. doi: 10.6052/1000-0992-26-019.
Abstract: Fatigue life prediction and reliability analysis are crucial for ensuring the long-term safety of major equipment in service. Traditional research paradigms mainly rely on expert experience, mechanism modeling, and classical statistical analysis methods. However, due to an insufficient understanding of fatigue failure behavior, it is difficult for traditional research paradigms to guarantee accurate predictions when modeling complex fatigue damage evolution. Represented by machine learning (ML), data-driven methods have shown great potential in fatigue life prediction and reliability analysis due to excellent nonlinear fitting capabilities. The limitation of small-sample fatigue dataset and the inherent data-driven nature of ML models limit the generalization performance of ML, making them difficult to meet the safety assessment requirements for long-term service. The physics-informed machine learning (PIML) framework offers a novel modeling paradigm for fatigue life prediction and reliability analysis, driven by failure mechanisms and fatigue data. While retaining the powerful fitting capabilities of ML models, it could ensure the physical consistency of the PIML framework. This study comprehensively outlines the mechanism and data-driven methods for fatigue life prediction and reliability analysis, and discusses the extensions and applications from deterministic life prediction to reliability analysis in detail. This study systematically summarizes different modeling paradigms to embed prior physical knowledge into ML, and deeply analyzes the advantages of different modeling strategies. For the application range, the performance and applicable boundaries are clarified, including computational efficiency, interpretability, and generalization performance. Finally, the limitations of current fatigue life prediction and reliability analysis methods are systematically summarized to highlight potential development directions for creating advanced prediction models that ensure the service safety and structural integrity of major engineering equipment.
Zhu S P, Wang L Y, Yan M L, Luo C Q, Wang Q Y. Fatigue life prediction and reliability analysis: Mechanism and data-driven, deterministic and stochastic methods. AdvancesinMechanics, in press. doi: 10.6052/1000-0992-26-016.
Abstract: By explicitly parameterizing structural topologies with geometric variables, the moving morphable components (MMC) topology optimization method offers several notable advantages, including a reduced number of design variables, seamless compatibility with computer-aided design (CAD) systems, decoupling between topology description and analysis models, and convenient incorporation of manufacturing-related constraints. These features can significantly enhance the efficiency of structural design, which has attracted widespread attention since the method was first proposed. This review systematically presents the core theoretical framework and extension system of the MMC method. Starting from the initial technical formulation—Including structural representation based on super-elliptic equations, compliance-based objective functions, optimization formulations with volume constraints, sensitivity analysis, and key technical issues—It further reviews multidimensional extensions encompassing geometric description, numerical techniques, and optimization solvers. Based on an analysis of the theoretical evolution of the method, this paper also reviews MMC-based solution strategies for specific optimization challenges such as nonlinear behavior, multi-material design, and stress-constrained optimization. In addition, interdisciplinary applications of the MMC method are summarized in areas including lightweight structural design, dynamic performance optimization, and metamaterial/metastructure design. Finally, in view of current research bottlenecks, several important future research directions are discussed, and the broad prospects of the MMC method in the era of intelligent computation are envisioned.
Li Z H, Chen W Q. Moving morphable components topology optimization approach: Extensions, applications, and prospects. AdvancesinMechanics, in press. doi: 10.6052/1000-0992-26-012.
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