Table of Content

18 June 2026, Volume 47 Issue 6

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Deformative response of bilayer films to spatially non-uniform stimuli

Zijing ZHANG, Gesa ZHANG, Haimin YAO

2026, 47(6):  1205-1214.  doi:10.1007/s10483-026-3396-6

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Bilayer films are widely employed as actuators because of their ability to undergo bending deformations in response to environmental stimuli. While the bending curvature induced by uniform stimuli can be accurately described by the classical Stoney formula, predicting the deformation of bilayer films under spatially non-uniform stimuli remains challenging. The difficulty lies mainly in the coupling between the film’s responsive deformation and the local stimulus intensity that it experiences. To address this challenge, in this study, we extend the classical Stoney relation by developing a theoretical framework that links the local curvature of the film to the space-dependent stimulus intensity. This framework enables the precise prediction of the deformed configurations of bilayer films subjected to complex, non-uniform stimulus fields. The theoretical results are validated through finite-element simulations and experimental measurements, demonstrating excellent agreement. Our findings provide a solid theoretical foundation for controlling the responsive deformation of bilayer actuators to spatially varying stimuli, which facilitates the application and development of soft thin-film actuators.

Nonlinear coupling mechanism of quasi-zero-stiffness units in multi-level structures

Shaokun YANG, Xingxing SHI, Xingzhong WANG, Jiuhui WU, Fuyin MA

2026, 47(6):  1215-1240.  doi:10.1007/s10483-026-3392-6

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Multilayer structures composed of quasi-zero-stiffness (QZS) units exhibit mechanical characteristics distinct from those of a single unit, and their behaviors are governed by the coupling mechanism between the QZS units. This paper introduces the coupling coefficient to quantitatively describe this mechanism, classifying the system into strongly coupled and weakly coupled states. Through theoretical analysis, numerical simulation, and experimental testing, the static and dynamic responses under different coupling states are comparatively investigated. The results show that in the strongly coupled system, the deformation behavior of each QZS unit shows high consistency, leading to a wider QZS region, weaker nonlinear characteristics, and stronger dynamic response. In the weakly coupled systems, the low degree of deformation coordinations among the units results in different QZS regions, enabling low-frequency vibration isolation under varying loads. The analytical approach of the coupling mechanisms and the static and dynamic response behaviors generated by the two coupling mechanisms provide guidance for the structural design of multifunctional and highly adaptable multi-level QZS metamaterials.

Analysis of competing toughening mechanisms in interlocked bio-inspired glass composites

Jiani JIANG, Qi WANG, Shuiqiang ZHANG, Dongli SHI, Li DING, Bingbing AN, Dongsheng ZHANG

2026, 47(6):  1241-1262.  doi:10.1007/s10483-026-3394-8

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Conventional ceramics and glasses exhibit high strength and stiffness; however, their inherent brittleness often leads to catastrophic fracture under mechanical loading. To overcome this limitation, natural materials such as nacre and sutures offer a compelling structural blueprint. Inspired by these natural architectures, a bio-inspired composite system that integrates a brick-and-mortar arrangement with a geometrically interlocked suture interface is developed. Uniaxial tensile experiments demonstrate that this hybrid design effectively combines nacre-like interfacial sliding with geometric interlocking, resulting in synergistic mechanical enhancements. To further elucidate the underlying deformation and failure mechanisms, comprehensive numerical simulations of the tensile behavior in glass-polymer bioinspired composites are carried out. Key micromechanical processes considered in the calculation include the frictional pull-out of glass interlocking structures, plastic deformation of the polymer matrix, and debonding at the composite interface. The failure of the composites is controlled by the competition between the geometric interlocking of the glass, the plastic deformation of the polymer matrix, and the interface debonding of the composite material. Increasing the interlocking angle and interfacial friction coefficient significantly elevates the tensile strength by promoting the frictional resistance during pull-out. A strong interfacial strength and a large failure displacement enhance the effective toughness of the interface, which promotes stable and progressive damage evolution, leading to improved overall mechanical properties. In contrast, the yield strength of the polymer matrix has no significant influence on the peak tensile strength in the present design configuration. It is also found that the interlocking with strong friction interaction and strong interface can activate significant energy-dissipation mechanisms, thereby significantly enhancing the toughness of the composites.

Symmetry-breaking mechanism in viscoelastic recovery time of curved nanobeams under time-varying loads

Xiuquan WANG, Nenghui ZHANG, Hanlin LIU, Jiawei LING, Qiqi LI

2026, 47(6):  1263-1278.  doi:10.1007/s10483-026-3389-7

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The dissipative characteristics of deformation recovery in curved nanobeams are crucial for micro/nano-device reliability. In situ experiments reveal the dependence of recovery characteristics on loading direction, but existing theories fail to elaborate this mechanism, and efficient prediction methods are scarce. This study proposes an elastic-viscoelastic core-shell model under Kirchhoff’s small deformation hypothesis, accounting for surface-inner dissipation and geometric differences. Using the time-domain differential method, we convert the integral model into an equivalent differential model and derive an analytical solution for the deformation recovery. Combined with finite element (FE) analysis, we study the load/geometric effects on the viscoelastic recovery of the nano-circular-arc. The results agree well with the experimental results and the FE simulations. They show that laminated structures and surface dissipation endow the recovery process with two intrinsic characteristic time scales and two stages, including an instantaneous jump and long-term evolution, in which the synergy and competition between bending and axial deformation cause the dependence of recovery behavior on the loading direction and symmetry-breaking phenomena. This study clarifies experimental mechanisms and provides a new dissipation control approach.

Asteroid impact trajectory based on Jupiter-perturbed Sun-Earth planar bicircular restricted four-body problem invariant manifolds

Meiling LI, Yingjing QIAN, Wenxue CHEN, Yan SHEN, Yue LIU

2026, 47(6):  1279-1300.  doi:10.1007/s10483-026-3390-8

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This paper proposes a novel low-energy impact trajectory design framework for near-Earth asteroids (NEAs), exploiting the dynamical properties of invariant manifolds within a Jupiter-perturbed Sun-Earth planar bicircular restricted four-body problem (RFBP). First, we investigate the influence of Jupiter’s perturbation on the instantaneous Jacobi constant C, which governs the evolutionary behavior of the zero-velocity curves. An energy mechanism is then established to link the instantaneous C with the feasible region for asteroid entry into the Earth-Moon sphere of influence (EMSOI). Using this mechanism, a screening procedure is developed to identify potential Earth-impacting asteroids by analyzing their accessible impact regions. Subsequently, low-energy impact trajectories are designed by joining unstable manifolds and the Lambert transfer, which is further optimized via the particle swarm optimization (PSO) algorithm. Finally, the numerical simulations conducted for asteroids 2010 XC15 and 2023 JD6 demonstrate that the proposed method significantly reduces propellant consumption. Overall, this study provides a practical and low-energy strategy for asteroid defense and deep-space mission design.

A nonlinear damping absorber for broadband and multi-directional vibration suppression

Haiting ZHENG, Hu DING, J. C. JI

2026, 47(6):  1301-1322.  doi:10.1007/s10483-026-3395-9

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Most existing vibration absorbers are limited by the need for precise tuning, and are difficult to suppress broadband vibration. A nonlinear damping absorber (NDA) is proposed in this paper to control the vibrations of structures in multiple modes, providing nonlinear damping in multiple directions and enabling broadband and multi-directional vibration suppression. A pipe is selected as the research object to analyze its dynamic behaviors and vibration suppression mechanisms. The vibration reduction performance of the NDA on the in-plane vibration and out-of-plane vibration of the pipe is studied through experimentation and theory. First, the configuration of the NDA is designed, and its mechanical model is established. An experimental platform is built for the parameter identification and multi-directional vibration reduction test of the absorber. Second, based on the generalized Hamilton’s principle, the mechanical model describing the in-plane vibration and out-of-plane vibration of the pipe with the NDAs is derived. The approximate solution of the nonlinear response is derived and numerically validated. The multi-directional and multi-modal vibration reduction efficiency of the NDAs for the structures is analyzed. The research results show that the proposed absorber can significantly control the multi-directional vibration. Nonlinear damping effectively broadens the vibration reduction bandwidth, and improves the damping efficiency, with the cubic term playing the dominant role. Finally, a concept of multi-modal weighted optimization is proposed. The absorber parameters are optimized through the particle swarm optimization (PSO) algorithm. This paper provides a new type of absorbers for the vibration control of multiple directions in broadband.

Crystal plasticity modeling of low-cycle fatigue in 6061-T6 aluminum alloy

Junsong HU, Ruijie DENG, Pan WANG

2026, 47(6):  1323-1340.  doi:10.1007/s10483-026-3400-6

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The 6061-T6 aluminum alloy is widely used in structural components under cyclic loading. This study investigates the low-cycle fatigue (LCF) behavior of this alloy through strain-controlled experiments combined with a multiscale crystal plasticity finite element (CPFE) framework. The fatigue crack nucleation life constituted a nearly consistent fraction of total life over the investigated strain amplitudes. A thermally activated slip-based model incorporating dislocation density as an internal state variable was implemented by backward Euler discretization and accurately reproduced experimental hysteresis loops. The CPFE simulations show that increasing strain amplitudes accelerates dislocation accumulation, with pile-ups preferentially occurring in regions of high grain boundary density. Orientation-dependent grain responses generate stress gradients and strain incompatibilities that promote crack initiation, while the peak accumulated equivalent plastic strain consistently localizes near grain boundaries. An extreme value statistical approach using the accumulated equivalent plastic strain as the fatigue indicator parameter (FIP) successfully predicts fatigue lives in agreement with experimental data. The simulations including brittle iron-rich intermetallic particles further reveal that particle-matrix property mismatch induces strong interfacial stress concentrations, where dislocation pile-ups trigger localized plasticity and preferential crack initiation. These multiscale simulations provide valuable insights for the structural integrity assessment and microstructure-informed design of fatigue-resistant aluminum alloys.

Intelligent surrogate modeling for penetration prediction: solving forward and inverse problems with multi-fidelity data

Danning JING, Xuguang CHEN, Shuo WANG, Qinglin WANG, Jie LIU, Xinhai CHEN

2026, 47(6):  1341-1362.  doi:10.1007/s10483-026-3397-7

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The analysis of penetration mechanics is critical for the offensive targeting and defensive design of underground facilities. Although computational methods are fundamental to penetration analysis, they are often constrained by a trade-off between accuracy and computational efficiency. Emerging artificial intelligence (AI) methods, with inherent strengths in modeling complex high-dimensional relationships from available data, provide promising alternatives for building intelligent surrogate models. This study proposes a fusion-enhanced radial basis function network (FE-RBFN) for penetration prediction, solving forward and inverse problems with multi-fidelity data. FE-RBFN employs three interconnected subnetworks to extract features and capture nonlinear correlations at varying fidelity levels. To overcome the challenge of data scarcity, FE-RBFN embeds a data fusion strategy to fully leverage multi-fidelity data from multiple sources. The experimental results demonstrate that our network yields rapid and precise predictions, outperforming traditional machine learning methods. Notably, in multi-fidelity scenarios, FE-RBFN exhibits robust prediction accuracy despite the limited availability of high-fidelity data.

A novel multi-material topology design automation algorithm for a customized MATLAB and Rhino-Grasshopper plugin with a generalized solid isotropic material with penalization

T. T. BANH, E. DAMTSAS, H. P. BAN, M. HERRMANN, D. LEE

2026, 47(6):  1363-1382.  doi:10.1007/s10483-026-3391-9

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Topology optimization (TO) plays an increasingly pivotal role in contemporary structural engineering, particularly in architectural realms. Despite Grasshopper’s prevalence in architectural design, the seamless integration of structural optimization, especially with multiple materials, has remained a persistent challenge in prior research. To address this gap, this paper introduces a novel solution: Stag, a multi-material plugin for the Grasshopper ecosystem of Rhinoceros 3D. Stag effortlessly integrates multi-material analyses into workflow design by leveraging the generalized solid isotropic material with penalization (SIMP) algorithm. Tailored for architectural modeling, construction, and prototyping, Stag sets a new standard for comprehensive plugins in a familiar software environment. Moreover, this paper illustrates the seamless compatibility between Grasshopper and the generalized SIMP-based approach, utilizing MATLAB for optimization. This lays the foundation for the future development of intricate customized multi-material plugins. Designed with user-friendliness in mind, Stag provides architects and designers with an intuitive platform to efficiently optimize the material distribution within intricate structures. As part of our commitment to accessibility, the Stag plugin is freely accessible on the Food4Rhino platform, ensuring its widespread adoption and usability.

Solving high-dimensional global optimization problems via solution space restructuring with neural network

N. VO, T. LE-DUC, H. TANG, H. NGUYEN-XUAN, S. H. LEE, J. H. LEE

2026, 47(6):  1383-1400.  doi:10.1007/s10483-026-3393-7

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It is well-known that appropriately determining the solution space and initializations is crucial for obtaining high-quality optimal solutions for optimization problems, considering both gradient-based and gradient-free techniques. However, the general framework for adaptively dealing with a particular optimization problem is commonly overlooked and thus still hidden in the literature. To overcome this limitation, a new approach assisted by the neural network (NN) is proposed for solving high-dimensional optimization issues. By restructuring the search space to optimize the objective function via a nonlinear mapping constructed by an autoencoder (AE), the surrogate solution space is constructed by a network training process and dynamically oriented to the optimal solution of the optimization issue. To enhance the optimization efficiency and address non-smooth problems, the classical metaheuristic grey wolf optimizer (GWO) and the adaptive moment estimation (Adam) are sequentially employed to complement the disadvantages of the constituted models. The effectiveness of the proposed approach is validated by solving a set of mathematical functions with 1 000-dimensional and three large-scale truss design optimization problems. Several numerical experiments show that the solution space is reduced in terms of both size and complexity based on the restructuring procedure, in which the global optimal solution is still conserved, leading to better optimization efficiency when solving optimization problems with complex search domains with large dimensions. In addition, the hybrid optimizer has also been proven to be more effective when combined with the restructuring technique owing to the use of the Adam algorithm in the second phase.

Adaptive wavelet multi-resolution solution for one-dimensional Burgers’ equation at high Reynolds numbers

Jihong ZHENG, Jizeng WANG, Youhe ZHOU, Xiaojing LIU

2026, 47(6):  1401-1416.  doi:10.1007/s10483-026-3398-8

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The wavelet multi-resolution interpolation Galerkin method (WMIGM) is combined with a mixed explicit-implicit time-stepping scheme to solve the one-dimensional Burgers’ equation at high Reynolds numbers, where the solutions exhibit evolving steep local gradients. In the proposed framework, a dynamic sequence of node distributions with local multi-resolution refinement is adaptively constructed according to the gradient information identified by a wavelet transform. The approximate solution at previous time levels, required in the time-stepping procedure, is represented by the same wavelet expansion used in its original construction, thereby eliminating the need for interpolation between different node distributions. Several representative numerical examples are presented to assess the accuracy, convergence, and robustness of the proposed adaptive wavelet method. The results demonstrate that the proposed approach possesses a higher accuracy and a faster convergence rate than many existing numerical methods, and can accurately capture complex shock dynamics without spurious oscillations, including boundary layer formation from smooth initial profiles and shock merging processes.

AI-driven triple-optimization based on ant colony optimization for minimizing deformation energy in three-dimensional analysis of bottom-hole assemblies

Qinfeng DI, Dakun LUO, Heyuan YANG, Tianxin LI, Wenchang WANG, Feng CHEN, H. ZHANG

2026, 47(6):  1417-1432.  doi:10.1007/s10483-026-3399-9

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An accurate analysis of the three-dimensional (3D) deformed configuration of a bottom-hole assembly (BHA) is critical for predicting and controlling well paths in directional drilling. Among the various numerical approaches, the weighted residual method exhibits superior performance owing to its semi-analytical nature, enabling high accuracy in handling diverse boundary conditions. In previous studies, the weighted residual method has been coupled with a dual optimization process to determine the 3D deformation and tangency point of the BHA. However, its applicability is limited by the conventional treatment of contact interactions between the BHA and wellbore wall. Specifically, stabilizer-wellbore contacts are regarded as predefined boundary conditions, rather than solving these contact positions as unknown variables consistent with actual downhole conditions. This limitation reduces modeling fidelity in complex downhole environments. To address this limitation, this study enhances the optimization-based weighted residual method by introducing ant colony optimization (ACO) to solve the 3D contact problem. In the proposed framework, the bending energy of the deformed BHA is conceptualized as “food”, while the contact positions and orientations of stabilizers are assigned a measure of “taste”. Through this metaphor, the ACO algorithm employs artificial “ants” to explore the optimal stabilizer locations and orientations that minimize the BHA bending energy, thereby refining the computed 3D deformation. The simulation results demonstrate that integrating ACO into the previously established dual optimization framework enables the effective determination of the contact configuration between the BHA and wellbore wall. As a result, the overall accuracy of the 3D BHA deformation analysis is significantly improved. In one representative case study, the bending energy of the BHA is reduced by 55.6% compared with that obtained from the original dual-optimization method.