2026 Vol.16(1)

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Research Article
Large eddy simulations of hypersonic boundary layer transition on a HyTRV model with upstream wall blowing/suction
Xuecheng Sun, Changping Yu, Xinliang Li, Chuanhong Zhang
Theoretical and Applied Mechanics Letters  16 (2026) 100619. doi: 10.1016/j.taml.2025.100619
[Abstract](362) [PDF 3913KB](10)
Abstract:
To investigate the effect of wall blowing/suction on hypersonic boundary layer transition, large eddy simulation is employed to analyze the HyTRV model under an incoming flow with a Mach number of 6 and a unit Reynolds number of 107 m−1. The model has a length of 1600 mm, and wall blowing/suction is applied to the windward surface’s upstream region (450–750 mm from the leading edge). The computational results indicate that upstream blowing accelerates the destabilization and breakdown of the streamwise vortex, promotes earlier transitions in the windward vortex region, and enhances the turbulent fluctuation intensity in the outer boundary layer. Conversely, upstream suction delays the transition and suppresses turbulent fluctuations in the outer boundary layer zone. The pressure fluctuation spectra are analyzed at different streamwise positions. The results demonstrate that upstream blowing significantly amplifies the development of a disturbance wave with a frequency of approximately 33 kHz at x = 1100 mm on the windward side. This frequency is hypothesized to correspond to the streamwise vortex instability mode. In contrast, upstream suction markedly suppresses the preexisting spectral peak near 38 kHz. Spectral proper orthogonal decomposition (SPOD) is applied to the streamwise/wall-normal temperature field. The results revealed that upstream blowing substantially increases the energy contribution of the first SPOD mode at a characteristic frequency of 32.55 kHz.
Design of a high-speed, low-turbulence water flume with initial application to free surface turbulent wake flow
David Butler, Skinder Dar, Minh Nguyen, Kaiqi Zhou, Chukwudum Eluchie, Cong Wang
Theoretical and Applied Mechanics Letters  16 (2026) 100621. doi: 10.1016/j.taml.2025.100621
[Abstract](379) [PDF 2835KB](0)
Abstract:
Despite the substantial progress of numerical methods in fluid mechanics, the complex multi-scale, multi-phase nature of turbulent flows continues to necessitate high-fidelity experimental data. As such, the development of a free-surface water tunnel (i.e. flume) capable of delivering high-speed, low-turbulence, free-surface flows is essential for fundamental research for marine applications. We report the design specifications and performance of a water flume recently constructed at the University of Iowa. The flume delivers high-speed (1.6 m/s), low-turbulence (<1.6%) uniform flows in an 8 m test section. The superior performance in delivering and maintaining well-conditioned flows over an extended test section is due to the properly designed upstream and downstream diffusers and the flow conditioners within. An additional high volumetric rate fluorescent dye visualization system was developed and employed for applications that challenge advanced laser-based measurement, particularly near the free-surface. The capability of the flume and associated instrumentation are demonstrated through an on-going investigation of the turbulent wake flow behind a surface-piercing 2D triangular wedge, revealing near free-surface coherent structures such as delayed vortex shedding and vortex-coupled, air-entrained tubes at high Froude numbers. The reported design details, in particular, the extended test section and downstream diffuser, will guide researchers developing similar hydrodynamic facilities for fundamental research.
A three-dimensional statistical damage model for rock-like materials based on principal stress action
Jun Xu, Sen Luo, Shihe Sun
Theoretical and Applied Mechanics Letters  16 (2026) 100625. doi: 10.1016/j.taml.2025.100625
[Abstract](440) [PDF 2760KB](5)
Abstract:
Principal stress plays a critical role in the deformation and failure process of rock or rock-like materials. However, existing studies indicate that the construction of a damage model based on principal stresses for describing the entire process of three-dimensional rock fracturing is subject to certain limitations and inadequacies. In this study, an innovative three-dimensional statistical damage constitutive model is developed by integrating the principal stress effect with the Gamma distribution function. This model effectively captures the complete damage evolution process of rock materials with initial defects through the introduction of a compaction correction coefficient and a residual strength correction term. Notably, the simulation accuracy is significantly enhanced in both the initial compaction stage and the post-peak residual strength stage. The parameter θ serves as an indicator of the material brittle-to-ductile transition, whereas the parameter k reflects the material’s strength characteristics. The parameter calibration process consists of three steps: determining the θ value on the basis of the rock brittleness index, deriving the k parameter from the k value growth curve, and finally establishing the peak-residual strength prediction equation under given confining pressure conditions. Compared with the traditional statistical damage model based on the Weibull distribution, this model not only features clear physical significance and a simplified calculation procedure but also contributes to the advancement of the three-dimensional damage fracture theory system for rock mechanics. Moreover, it offers a robust framework for evaluating the mechanical response of rocks under varying confining pressures, which has significant implications for safe design and risk assessment in civil engineering or rock engineering.
Non-equilibrium evaporation of Lennard-Jones fluids: Enskog-Vlasov equation and Hertz-Knudsen model
Shaokang Li, Livio Gibelli, Yonghao Zhang
Theoretical and Applied Mechanics Letters  16 (2026) 100628. doi: 10.1016/j.taml.2025.100628
[Abstract](340) [PDF 1212KB](2)
Abstract:
Enskog-Vlasov equation is currently the most sophisticated kinetic model for describing non-equilibrium evaporative flows. While it enables more efficient simulations than the molecular dynamics (MD) methods, its accuracy in reproducing the flow properties of real fluids is limited by both the assumptions underlying the Vlasov forcing term and the approximation introduced by the Enskog collision term for short-range molecular interactions. To address this limitation, this work proposes a molecular kinetic model specifically designed for real fluids, with the Lennard-Jones fluids as an example. The model is first applied to evaluate the equilibrium characteristics of a liquid-vapour system, including the liquid-vapour coexistence curve, transport coefficients, vapour pressure, and surface tension coefficient. The results show excellent agreement with the MD simulation and experimental data. Furthermore, the model is used to investigate non-equilibrium evaporation, with a particular focus on the velocity distribution function adjacent to the liquid-vapour interface. The results confirm that deviations from the Maxwellian distribution persist in the vapour region, indicating limitations of the classical Hertz-Knudsen relation under pronounced non-equilibrium conditions. This work represents a critical step towards the development of an accurate and efficient computational framework for modelling non-equilibrium liquid-vapour flows for real fluids, with direct relevance to practical applications such as flow cooling.
Continuum modeling for layer jamming structures
Shuai Zhang, Jiantao Yao, Shizeng Li, Xinbo Chen
Theoretical and Applied Mechanics Letters  16 (2026) 100633. doi: 10.1016/j.taml.2025.100633
[Abstract](264) [PDF 2906KB](0)
Abstract:
Layer jamming structures (LJS) are a class of variable stiffness structures that are valuable for adaptive and soft robotic systems. However, existing models for LJS often rely on discrete approximations or are tailored to specific configurations, limiting their generalizability and computational efficiency. In this study, we propose a continuum elastoplastic constitutive model for LJS based on the average-field technique. The model captures both the jamming (no interlayer slipping) and slipping states of LJS, enabling analytical expressions for yield criteria, and dissipated energy density. Finite element simulations in Abaqus incorporating periodic boundary conditions were conducted to validate the theoretical model under various deformation scenarios, including uniaxial shear, multi-directional shear, and coupled shear-normal loading. The results demonstrate strong agreement between numerical and theoretical predictions, effectively capturing the nonlinear transitions in stiffness and energy evolution. This continuum framework offers a unified, scalable tool for modeling the mechanical behavior of LJS and supports the design and optimization of stiffness-tunable systems in soft robotics and beyond.
Predicting stress and damage in carbon fiber-reinforced composites deformation process using composite U-net surrogate model
Zeping Chen, Marwa Yacouti, Maryam Shakiba, Jian-Xun Wang, Tengfei Luo, Vikas Varshney
Theoretical and Applied Mechanics Letters  16 (2026) 100634. doi: 10.1016/j.taml.2025.100634
[Abstract](252) [PDF 6565KB](0)
Abstract:
Research highlightsCarbon fiber-reinforced composites (CFRC) are pivotal in advanced engineering applications due to their exceptional mechanical properties. A deep understanding of CFRC behavior under mechanical loading is essential for optimizing performance in demanding applications such as aerospace structures. While traditional finite element method (FEM) simulations, including advanced techniques like interface-enriched generalized FEM (IGFEM), offer valuable insights, they can struggle with computational efficiency. Existing data-driven surrogate models partially address these challenges by predicting propagated damage or stress-strain behavior but fail to comprehensively capture the evolution of stress and damage throughout the entire deformation history, including crack initiation and propagation. This study proposes a novel auto-regressive composite U-net deep learning model to simultaneously predict stress and damage fields during CFRC deformation. By leveraging the U-net architecture’s ability to capture spatial features and integrate macro- and micro-scale phenomena, the proposed model overcomes key limitations of prior approaches. The model achieves high accuracy in predicting the evolution of stress and damage distribution within the microstructure of a CFRC under unidirectional strain, offering a speed-up of over 150 times compared to IGFEM.
Trajectory parameter identification and impact point prediction for canard dual-spin projectile considering nonlinear effects
Xinxin Zhao, Jinguang Shi, Zhongyuan Wang
Theoretical and Applied Mechanics Letters  16 (2026) 100635. doi: 10.1016/j.taml.2025.100635
[Abstract](238) [PDF 2728KB](2)
Abstract:
Canard dual-spin projectiles typically adjust the forebody roll angle for trajectory correction by analyzing deviations between predicted impact points and target positions. An accurate method for trajectory parameter identification and impact point prediction is crucial for this process. This paper introduces nonlinear factors to couple geometric and aerodynamic nonlinear effects at large angles of attack, analyzes angular motion dynamics before and after control initiation, as well as their influence on center-of-mass motion, thereby establishing an improved modified point-mass trajectory equation for such projectiles. Moreover, by mapping the effects of random disturbances and canard-body interactions to a finite set of primary characteristic parameters and employing periodic averaging to suppress fluctuations caused by rapid period changes of the complex angle of attack after control initiation, a nonlinear trajectory filtering model for both uncontrolled and controlled flights is proposed using the unscented Kalman filter algorithm, with its performance in parameter identification and impact point prediction systematically evaluated. Numerical results indicate that the improved modified point-mass trajectory equation accurately characterizes the nonlinear effects of canard control disturbances on aerodynamics and trajectory compared to traditional methods, closely matching rigid body trajectories for both uncontrolled and controlled flight, while improving computational efficiency by three orders of magnitude to meet real-time requirements. Furthermore, the filtering model effectively predicts uncontrolled trajectories and significantly reduces the influence of canard control initiation and orientation changes on prediction accuracy during controlled flight, thereby providing a theoretical foundation for studying correction strategies and guidance control methods, particularly for multiple control initiations.
Topographic control of gyre dynamics under thermal and wind forcing in rotating stratified systems
Jinichi Koue
Theoretical and Applied Mechanics Letters  16 (2026) 100643. doi: 10.1016/j.taml.2025.100643
[Abstract](239) [PDF 7892KB](0)
Abstract:
Topographic features exert fundamental control on large-scale oceanic circulation, yet their role under the combined influence of thermal and wind forcings remains insufficiently understood. Here, rotating tank experiments in stratified fluids are employed to investigate how slopes and depressions modulate gyre dynamics. Thermal forcing alone generated seasonally reversing surface circulations: summer heating induced robust counterclockwise gyres, whereas winter cooling produced clockwise circulation. These seasonal patterns were amplified near slopes and depressions owing to localized heat retention. In tanks with depressions, surface velocities weakened, giving rise to seasonally reversing, localized vortices. Under wind forcing, persistent counterclockwise gyres developed, with their centers displaced offshore by spatial heterogeneity in wind stress. Depressions generated pressure minima that drew fluid inward, producing centrally confined counterclockwise eddies shaped by the Coriolis force. When thermal and wind forcings act simultaneously, gyres markedly intensify, resulting in enhanced vorticity near the thermocline and flow suppression at depth due to stratification. Strikingly, the observed velocities exceeded the linear superposition of the individual forcings, demonstrating a nonlinear interaction. These results underscore the decisive role of small-scale topography in modulating rotating, stratified flows and provide mechanistic insights into the dynamics of basin-scale circulation in natural water bodies.
Nonlinear coupling from acoustics to aerodynamics in perforated plates at normal incidence
Sylvain C. Humbert
Theoretical and Applied Mechanics Letters  16 (2026) 100647. doi: 10.1016/j.taml.2025.100647
[Abstract](212) [PDF 1810KB](0)
Abstract:
This study addresses the mean nonlinear pressure loss through a perforated plate caused by the combination of the steady bias flow itself and high-amplitude acoustic excitations. An analytical treatment of this problem yields an explicit formula allowing one to estimate the mean flow resistance as a function of the steady flow velocity and unsteady velocity amplitudes. An increase in the unsteady velocity amplitude(s) yields an increase in the mean flow resistance, which highlights the presence of nonlinear coupling from acoustics to aerodynamics. For a given value of the mean flow velocity (or pressure drop), this causes an increase in the mean pressure loss (or a decrease in the steady flow velocity). The model highlights that for moderate acoustic disturbances, the mean flow and acoustic contributions to the mean flow pressure loss add up, whereas for large acoustic velocity amplitudes, the pressure loss is, to the leading order, proportional to the product of the mean flow velocity and the maximum acoustic velocity amplitude. Finally, the model is exploited to explain the presence in some acoustic studies of a valley in the acoustic resistance curve versus the acoustic velocity amplitude. The simplicity of the model makes it attractive to account for 1D flow oscillation effects in fluid flow network models, to understand the essential mechanisms at play in the acoustically induced increase in the mean flow resistance, and to take this phenomenon into account when estimating the acoustic impedance of perforated plates.
Decoupling analysis of perturbed and unrelaxed elastic tension in viscoelastic swirling liquid jets
Yiqian Xu, Kai Mu, Ting Si
Theoretical and Applied Mechanics Letters  16 (2026) 100659. doi: 10.1016/j.taml.2026.100659
[Abstract](192) [PDF 2040KB](2)
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Linear instability analysis and energy budget analysis are carried out to investigate the instability of viscoelastic swirling liquid jets, with a main focus on the decoupling effects of unrelaxed axial/azimuthal elastic tensions and the elastic tension caused by perturbation development. First, the effect of perturbed elastic tension is studied by varying the polymer relaxation time while keeping the axial and azimuthal unrelaxed elastic tensions absent. It is found that the perturbed elastic tension stabilizes the swirling liquid jet, with its influence being weakened as the polymer relaxation time increases. The combined effects of perturbed elastic tension, centrifugal force, surface tension and viscous dissipation could promote jet instability and facilitate the predominant mode transition to larger azimuthal wavenumbers. Then, the effects of unrelaxed azimuthal and axial elastic tension are examined separately. The unrelaxed azimuthal elastic tension has little effect on the modes with small azimuthal wavenumbers (i.e., ) but could significantly suppress the instabilities of the modes with large azimuthal wavenumbers (i.e., ). In addition, the increase in unrelaxed azimuthal elastic tension could promote the predominant mode transition to smaller azimuthal wavenumbers. In contrast, the unrelaxed axial elastic tension could greatly suppress the instabilities of the modes with small azimuthal wavenumbers () but only has a negligible effect on the modes with large azimuthal wavenumbers ().
Multi-objective optimization and biomechanical injury analysis of rear-seat occupant restraint systems in small overlap collision
Jia Yu, Jingyu Xu, Tao Xiong, Meng Xu, Hao Deng, Zhiyong Yin, Xiuju Yang, Shengxiong Liu
Theoretical and Applied Mechanics Letters  16 (2026) 100661. doi: 10.1016/j.taml.2026.100661
[Abstract](169) [PDF 2653KB](1)
Abstract:
In small overlap collision, rear-seat occupants face elevated injury risks. This study conducts multi-objective optimization of the rear-seat occupant restraint system to reduce these injury risks and enhance overall vehicle safety performance. Based on real-world traffic accident data, a full-vehicle crash simulation model was established and validated with the actual injury data. Weighted injury criteria (WIC) and neck injury metrics () were selected as optimization objectives. The rear-seat restraint system was optimized using NSGA-II and TOPSIS algorithms to determine the optimal parameter configurations. The optimized parameters were subsequently reintegrated into the simulation model for validation. The results demonstrate a significant reduction in occupant injuries, with WIC and reduced by 30.3% and 20.7%, respectively.
Review
Artificial intelligence application in multiscale biomechanics
Erqian Xu, Jin Zhou, Yan Zhang, Qing Luo, Guanbin Song, Shouqin Lü, Mian Long
Theoretical and Applied Mechanics Letters  16 (2026) 100629. doi: 10.1016/j.taml.2025.100629
[Abstract](290) [PDF 1854KB](5)
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HighlightThe rapid development and widespread application of artificial intelligence (AI) technology have significantly improved understanding across various fields, including biomechanics. To deepen the understanding of AI applications in this field and explore future developments, this review focuses on the progress of AI in multiscale biomechanics. We first outline the progress history, fundamental principles, and typical models of AI. Next, we introduce the main applications of the two typical AI paradigms—data-driven and knowledge-driven—in the context of multiscale biomechanical studies. The first paradigm focuses primarily on predicting protein structure, interactions, and conformational dynamics at the molecular level, as well as on subcellular structure recognition, cell mechanics prediction and cell trajectory tracking at the cellular level. The second paradigm concentrates on biological fluid and solid mechanics at the tissue level. Finally, the existing issues and challenges faced by current AI technologies in biomechanics are discussed, and potential future issues are proposed from the perspective of informative integration.