Institute of Mechanics,
Chinese Academy of Sciences
2026 Vol.16(2)
column
Display Mode： |
Theoretical and Applied Mechanics Letters 16 (2026) 100609.
doi: 10.1016/j.taml.2025.100609
Abstract:
The hybrid neural differentiable models mark a significant advancement in the field of scientific machine learning. These models, integrating numerical representations of known physics into deep neural networks, offer enhanced predictive capabilities and show great potential for data-driven modeling of complex physical systems. However, a critical and yet unaddressed challenge lies in the quantification of inherent uncertainties stemming from multiple sources. Addressing this gap, we introduce a novel method, uncertainty quantification for hybrid neural differentiable modeling, for effective and efficient uncertainty propagation and estimation in hybrid neural differentiable models, leveraging the strengths of deep ensemble Bayesian learning and nonlinear transformations. Specifically, our approach effectively discerns and quantifies both aleatoric uncertainties, arising from data noise, and epistemic uncertainties, resulting from model-form discrepancies and data sparsity. This is achieved within a Bayesian model averaging framework, where aleatoric uncertainties are modeled through hybrid neural models. The unscented transformation plays a pivotal role in enabling the flow of these uncertainties through the nonlinear functions within the hybrid model. In contrast, epistemic uncertainties are estimated using an ensemble of stochastic gradient descent trajectories. This approach offers a practical approximation to the posterior distribution of both the network parameters and the physical parameters. Notably, our framework is designed for simplicity in implementation and high scalability, making it suitable for parallel computing environments. The merits of the proposed method have been demonstrated through problems governed by both ordinary and partial differentiable equations.
The hybrid neural differentiable models mark a significant advancement in the field of scientific machine learning. These models, integrating numerical representations of known physics into deep neural networks, offer enhanced predictive capabilities and show great potential for data-driven modeling of complex physical systems. However, a critical and yet unaddressed challenge lies in the quantification of inherent uncertainties stemming from multiple sources. Addressing this gap, we introduce a novel method, uncertainty quantification for hybrid neural differentiable modeling, for effective and efficient uncertainty propagation and estimation in hybrid neural differentiable models, leveraging the strengths of deep ensemble Bayesian learning and nonlinear transformations. Specifically, our approach effectively discerns and quantifies both aleatoric uncertainties, arising from data noise, and epistemic uncertainties, resulting from model-form discrepancies and data sparsity. This is achieved within a Bayesian model averaging framework, where aleatoric uncertainties are modeled through hybrid neural models. The unscented transformation plays a pivotal role in enabling the flow of these uncertainties through the nonlinear functions within the hybrid model. In contrast, epistemic uncertainties are estimated using an ensemble of stochastic gradient descent trajectories. This approach offers a practical approximation to the posterior distribution of both the network parameters and the physical parameters. Notably, our framework is designed for simplicity in implementation and high scalability, making it suitable for parallel computing environments. The merits of the proposed method have been demonstrated through problems governed by both ordinary and partial differentiable equations.
Theoretical and Applied Mechanics Letters 16 (2026) 100636.
doi: 10.1016/j.taml.2025.100636
Abstract:
The behavior of materials is influenced by a wide range of phenomena occurring across various time and length scales. To better understand the impact of microstructure on the macroscopic response, multiscale modeling strategies are essential. Numerical methods, such as the -approach, account for micro-macro interactions to predict the global response in a concurrent manner. However, these methods are computationally intensive because of the repeated evaluations of the discretized microscale. This challenge has led to the integration of deep learning techniques into computational homogenization frameworks to accelerate multiscale simulations. In this work, we employ neural operators to predict microscale physics, resulting in a hybrid model that combines data-driven and physics-based approaches. This allows for physics-guided learning and provides flexibility for different materials and spatial discretizations. We apply this method to time-dependent solid mechanics problems involving viscoelastic material behavior, where the state is represented by internal variables only at the microscale. The constitutive relationships at the microscale are incorporated into the model architecture and the internal variables are computed on the basis of established physical principles. The results for homogenized stresses (% error) show that the approach is computationally efficient ( faster).
The behavior of materials is influenced by a wide range of phenomena occurring across various time and length scales. To better understand the impact of microstructure on the macroscopic response, multiscale modeling strategies are essential. Numerical methods, such as the -approach, account for micro-macro interactions to predict the global response in a concurrent manner. However, these methods are computationally intensive because of the repeated evaluations of the discretized microscale. This challenge has led to the integration of deep learning techniques into computational homogenization frameworks to accelerate multiscale simulations. In this work, we employ neural operators to predict microscale physics, resulting in a hybrid model that combines data-driven and physics-based approaches. This allows for physics-guided learning and provides flexibility for different materials and spatial discretizations. We apply this method to time-dependent solid mechanics problems involving viscoelastic material behavior, where the state is represented by internal variables only at the microscale. The constitutive relationships at the microscale are incorporated into the model architecture and the internal variables are computed on the basis of established physical principles. The results for homogenized stresses (% error) show that the approach is computationally efficient ( faster).
Theoretical and Applied Mechanics Letters 16 (2026) 100650.
doi: 10.1016/j.taml.2025.100650
Abstract:
This paper presents a new technology for copper wire processing. This technology involves deforming the wire in a rotating equal-channel stepped matrix, after which the workpiece is subjected to a drawing operation. As a result of the deformation of the copper alloy wire via this technology and subsequent annealing at 400 °C, a gradient microstructure with improved mechanical properties was obtained. Annealing after deformation is carried out to stabilize the formed submicrocrystalline structure, isolate dispersed strengthening particles and increase the electrical conductivity. The surface zone is crushed to 400 nm, and the intermediate zone is crushed to 2 μm. Then, the grain size increases further toward the central part of the wire and is 22 μm. The generation of a gradient-symmetrical microstructure was confirmed via microhardness tests. Thus, our method, which combines twisting in a rotating matrix and drawing, is a promising tool for obtaining materials with improved mechanical properties. It allows reducing drawing forces, obtaining a gradient structure of the material and increasing its plasticity.
This paper presents a new technology for copper wire processing. This technology involves deforming the wire in a rotating equal-channel stepped matrix, after which the workpiece is subjected to a drawing operation. As a result of the deformation of the copper alloy wire via this technology and subsequent annealing at 400 °C, a gradient microstructure with improved mechanical properties was obtained. Annealing after deformation is carried out to stabilize the formed submicrocrystalline structure, isolate dispersed strengthening particles and increase the electrical conductivity. The surface zone is crushed to 400 nm, and the intermediate zone is crushed to 2 μm. Then, the grain size increases further toward the central part of the wire and is 22 μm. The generation of a gradient-symmetrical microstructure was confirmed via microhardness tests. Thus, our method, which combines twisting in a rotating matrix and drawing, is a promising tool for obtaining materials with improved mechanical properties. It allows reducing drawing forces, obtaining a gradient structure of the material and increasing its plasticity.
Theoretical and Applied Mechanics Letters 16 (2026) 100611.
doi: 10.1016/j.taml.2025.100611
Abstract:
Direct numerical simulation of spatially developing turbulent boundary layers with periodic blowing or suction through a series of inclined slots in a control region was conducted. The wall-generated Reynolds shear stress (RSS), i.e., the RSS on the wall in the control region, is generated through the control scheme. The effect of the wall-generated RSS on friction drag was examined via a series of simulations. The Reynolds numbers of the turbulent boundary layers investigated vary from 300–860 on the basis of the external flow velocity and the momentum thickness. The proposed control scheme was used to verify the relationship between the wall-generated RSS and skin friction drag, and it was found that a wall-generated negative RSS (net positive) increases the skin friction drag, whereas a wall-generated positive RSS (net negative) reduces it. The proposed control method can provide a high drag reduction rate, and even negative resistance and backflow can be observed.
Direct numerical simulation of spatially developing turbulent boundary layers with periodic blowing or suction through a series of inclined slots in a control region was conducted. The wall-generated Reynolds shear stress (RSS), i.e., the RSS on the wall in the control region, is generated through the control scheme. The effect of the wall-generated RSS on friction drag was examined via a series of simulations. The Reynolds numbers of the turbulent boundary layers investigated vary from 300–860 on the basis of the external flow velocity and the momentum thickness. The proposed control scheme was used to verify the relationship between the wall-generated RSS and skin friction drag, and it was found that a wall-generated negative RSS (net positive) increases the skin friction drag, whereas a wall-generated positive RSS (net negative) reduces it. The proposed control method can provide a high drag reduction rate, and even negative resistance and backflow can be observed.
Theoretical and Applied Mechanics Letters 16 (2026) 100620.
doi: 10.1016/j.taml.2025.100620
Abstract:
Fluid mechanics holds an almost infinite range of unsolved questions whose answers could improve energy efficiency, environmental protection and public health. Yet progress is throttled by scarce resources—human expertise, time cost and research funding. We introduce turbulence.ai, the first fully autonomous AI scientist for fluid mechanics, designed to lift those constraints. A multi-agent architecture unifies hypothesis generation, computational fluid dynamics execution and draft writing. From a single natural-language query the platform (i) formulates testable ideas, (ii) orchestrates a series of numerical experiments, (iii) interprets results, and (iv) produces a draft. In end-to-end demonstrations, turbulence.ai autonomously generated two academic manuscripts and an article-based PhD thesis (cumulative dissertation). This advance inaugurates a new chapter in fluid-mechanics research and could expand human’s knowledge base by orders of magnitude.
Fluid mechanics holds an almost infinite range of unsolved questions whose answers could improve energy efficiency, environmental protection and public health. Yet progress is throttled by scarce resources—human expertise, time cost and research funding. We introduce turbulence.ai, the first fully autonomous AI scientist for fluid mechanics, designed to lift those constraints. A multi-agent architecture unifies hypothesis generation, computational fluid dynamics execution and draft writing. From a single natural-language query the platform (i) formulates testable ideas, (ii) orchestrates a series of numerical experiments, (iii) interprets results, and (iv) produces a draft. In end-to-end demonstrations, turbulence.ai autonomously generated two academic manuscripts and an article-based PhD thesis (cumulative dissertation). This advance inaugurates a new chapter in fluid-mechanics research and could expand human’s knowledge base by orders of magnitude.
Theoretical and Applied Mechanics Letters 16 (2026) 100624.
doi: 10.1016/j.taml.2025.100624
Abstract:
Flapping-wing aircraft, as a typical example of bionic aviation vehicles, hold significant importance in fields such as environmental monitoring, reconnaissance, and aerobiology research. However, the design of flapping-wing aircrafts usually relies on the imitation of birds or insects in nature and requires extensive iterative optimization. In this study, a computational fluid dynamics (CFD) data-driven flight optimization approach is developed for flapping-wing aircraft design. First, we conduct a bionic aerodynamic analysis of the unsteady flow field during the flapping motions and multiple cases with different combinations of flight parameters are simulated via CFD to investigate the factors influencing the flight performance. The simulation data are subsequently used to establish a deep neural network (DNN) model to explore the relationship between the flapping motions and the flight performance. Finally, optimization algorithms are applied to search for the optimal flight parameter combinations under different weights, which can provide a valuable reference for the overall design and flight optimization of flapping-wing aircraft.
Flapping-wing aircraft, as a typical example of bionic aviation vehicles, hold significant importance in fields such as environmental monitoring, reconnaissance, and aerobiology research. However, the design of flapping-wing aircrafts usually relies on the imitation of birds or insects in nature and requires extensive iterative optimization. In this study, a computational fluid dynamics (CFD) data-driven flight optimization approach is developed for flapping-wing aircraft design. First, we conduct a bionic aerodynamic analysis of the unsteady flow field during the flapping motions and multiple cases with different combinations of flight parameters are simulated via CFD to investigate the factors influencing the flight performance. The simulation data are subsequently used to establish a deep neural network (DNN) model to explore the relationship between the flapping motions and the flight performance. Finally, optimization algorithms are applied to search for the optimal flight parameter combinations under different weights, which can provide a valuable reference for the overall design and flight optimization of flapping-wing aircraft.
Theoretical and Applied Mechanics Letters 16 (2026) 100627.
doi: 10.1016/j.taml.2025.100627
Abstract:
REBa2Cu3O7-x (REBCO, RE: rare earth elements, such as Y and Gd, etc.) coated conductors (CCs) have been well commercialized. Conductor on round core (CORC) cables have been developed for transporting large direct current (DC) or alternating current (AC) currents over long distances. In this work, electromechanical models for CCs in a CORC structure were established, in which the effects of bending and deflection strains in the REBCO layer of a CC on the structural integrity and critical current density degradation during winding were considered. Compared with the previous model, which considers only the bending strain, the newly presented model agrees better with the experimental results, demonstrating that high winding angles and small diameters of round cores potentially result in severe degradation of the critical current. For the case of AC loss, the experimental results show that high winding angles increase AC loss, whereas the diameters of the former cores have little influence. The revised Norris model gives precise predictions for the applied AC currents close to the critical current but underestimates the losses for applied AC currents less than the critical current, especially for CCs that are wound at high angles. The established electromechanical models are expected to be beneficial for understanding the properties and optimizing the applications of CORC cables.
REBa2Cu3O7-x (REBCO, RE: rare earth elements, such as Y and Gd, etc.) coated conductors (CCs) have been well commercialized. Conductor on round core (CORC) cables have been developed for transporting large direct current (DC) or alternating current (AC) currents over long distances. In this work, electromechanical models for CCs in a CORC structure were established, in which the effects of bending and deflection strains in the REBCO layer of a CC on the structural integrity and critical current density degradation during winding were considered. Compared with the previous model, which considers only the bending strain, the newly presented model agrees better with the experimental results, demonstrating that high winding angles and small diameters of round cores potentially result in severe degradation of the critical current. For the case of AC loss, the experimental results show that high winding angles increase AC loss, whereas the diameters of the former cores have little influence. The revised Norris model gives precise predictions for the applied AC currents close to the critical current but underestimates the losses for applied AC currents less than the critical current, especially for CCs that are wound at high angles. The established electromechanical models are expected to be beneficial for understanding the properties and optimizing the applications of CORC cables.
Theoretical and Applied Mechanics Letters 16 (2026) 100630.
doi: 10.1016/j.taml.2025.100630
Abstract:
Collaborative technology for the remote, large-scale deployment of drones using dispersal systems holds significant potential in applications such as post-disaster rescue, which must balance low overload with high thrust, in addition to precisely controlling the separation attitude. To address these issues, this paper introduces a multi-gasbag propulsion system with a high aspect ratio that coordinates multiple gasbags to generate sufficient thrust. By adjusting the inlet size of the gasbag, the separation behavior of the release unit can be accurately controlled. A multidimensional two-phase flow model is established, accompanied by both combustion and flow experiments and a double-gasbag propulsion experiment. The results demonstrate that the proposed mathematical model is accurate, effectively captures the pressure fluctuations and spatiotemporal distribution of flow field parameters, and determines the separation attitude of the release unit. For the cases studied in this paper, the pressure at the gasbag inlet (z = 650 mm) is the dominant factor during the gasbag propulsion response, causing the release unit to rotate counterclockwise when the gasbag inlet sizes are identical. Increasing the inlet size at z = 50 mm compensates for the adverse effects of uneven axial pressure distribution, thereby achieving a neutral separation for the release unit. When the radii r₁ and r₂ vary between 2 and 12 mm, the angular velocity and attitude angle of the release unit are found to range from −15.50 to 15.20 rad/s and from −0.109 to 0.106 rad, respectively.
Collaborative technology for the remote, large-scale deployment of drones using dispersal systems holds significant potential in applications such as post-disaster rescue, which must balance low overload with high thrust, in addition to precisely controlling the separation attitude. To address these issues, this paper introduces a multi-gasbag propulsion system with a high aspect ratio that coordinates multiple gasbags to generate sufficient thrust. By adjusting the inlet size of the gasbag, the separation behavior of the release unit can be accurately controlled. A multidimensional two-phase flow model is established, accompanied by both combustion and flow experiments and a double-gasbag propulsion experiment. The results demonstrate that the proposed mathematical model is accurate, effectively captures the pressure fluctuations and spatiotemporal distribution of flow field parameters, and determines the separation attitude of the release unit. For the cases studied in this paper, the pressure at the gasbag inlet (z = 650 mm) is the dominant factor during the gasbag propulsion response, causing the release unit to rotate counterclockwise when the gasbag inlet sizes are identical. Increasing the inlet size at z = 50 mm compensates for the adverse effects of uneven axial pressure distribution, thereby achieving a neutral separation for the release unit. When the radii r₁ and r₂ vary between 2 and 12 mm, the angular velocity and attitude angle of the release unit are found to range from −15.50 to 15.20 rad/s and from −0.109 to 0.106 rad, respectively.
Theoretical and Applied Mechanics Letters 16 (2026) 100632.
doi: 10.1016/j.taml.2025.100632
Abstract:
Tungsten heavy alloys (W-Ni-Fe) have become critical materials in defense and aerospace applications due to their high density and superior mechanical properties, yet their constitutive models under dynamic loading remain incomplete. This study systematically investigates the mechanical behavior of a 95W-Ni-Fe-Co alloy fabricated through vacuum sintering, solution treatment, and rotary forging processes via quasi-static and dynamic compression testing. Microstructural characterization reveals that solution treatment significantly refines tungsten grains (30.5 μm vs. 45 μm in as-sintered state) while enhancing W/Co diffusion in the binder phase. Rotary forging introduces 20% plastic deformation, achieving 81% yield strength enhancement (1305 MPa vs. 720 MPa in as-sintered condition). Dynamic tests (1500 s−1−6500 s−1) demonstrate distinct strain rate strengthening effects: solution-treated alloy exhibits optimal strain hardening capacity (B=1693 MPa) with homogeneous deformation, whereas rotary-forged specimens show higher susceptibility to adiabatic shear instability due to localized deformation band initiation. A modified Johnson-Cook (MJC) model incorporating strain-strain rate coupling coefficients (C₁−C₅) reduces prediction errors to 2.3% (compared with 10%−30% errors from original JC model). Numerical simulations implemented through ABAQUS/VUMAT secondary development validate MJC model accuracy under high strain rates. These findings provide critical theoretical foundations and constitutive model support for tungsten alloy design under extreme service conditions, with future research focusing on fracture criteria and impact behavior investigation.
Tungsten heavy alloys (W-Ni-Fe) have become critical materials in defense and aerospace applications due to their high density and superior mechanical properties, yet their constitutive models under dynamic loading remain incomplete. This study systematically investigates the mechanical behavior of a 95W-Ni-Fe-Co alloy fabricated through vacuum sintering, solution treatment, and rotary forging processes via quasi-static and dynamic compression testing. Microstructural characterization reveals that solution treatment significantly refines tungsten grains (30.5 μm vs. 45 μm in as-sintered state) while enhancing W/Co diffusion in the binder phase. Rotary forging introduces 20% plastic deformation, achieving 81% yield strength enhancement (1305 MPa vs. 720 MPa in as-sintered condition). Dynamic tests (1500 s−1−6500 s−1) demonstrate distinct strain rate strengthening effects: solution-treated alloy exhibits optimal strain hardening capacity (B=1693 MPa) with homogeneous deformation, whereas rotary-forged specimens show higher susceptibility to adiabatic shear instability due to localized deformation band initiation. A modified Johnson-Cook (MJC) model incorporating strain-strain rate coupling coefficients (C₁−C₅) reduces prediction errors to 2.3% (compared with 10%−30% errors from original JC model). Numerical simulations implemented through ABAQUS/VUMAT secondary development validate MJC model accuracy under high strain rates. These findings provide critical theoretical foundations and constitutive model support for tungsten alloy design under extreme service conditions, with future research focusing on fracture criteria and impact behavior investigation.
Theoretical and Applied Mechanics Letters 16 (2026) 100637.
doi: 10.1016/j.taml.2025.100637
Abstract:
This work presents the application of a pseudo-elastic model to address the uniaxial compressive stress-strain behavior of expanded polystyrene foams. The model combines an Ogden-based hyperfoam formulation for the loading path of experimental testing with a damage-dependent approach for the unloading. The loading during compression is described using a simplified hyperfoam strain-energy function that effectively captures the nonlinear response of compressible polymer foams. For the unloading path, the model incorporates a scalar damage parameter controlled by three key variables: maximum damage, a damage evolution rate, and a transition parameter. Experimental validation confirms the model’s accuracy in predicting the mechanical response of polystyrene foams, including inelastic phenomena. This precision is supported by coefficient of determination R2 values close to unity when comparing the model’s predictions with experimental data. Thus, the proposed model provides a practical tool for analyzing the compressive stress response in polystyrene foams.
This work presents the application of a pseudo-elastic model to address the uniaxial compressive stress-strain behavior of expanded polystyrene foams. The model combines an Ogden-based hyperfoam formulation for the loading path of experimental testing with a damage-dependent approach for the unloading. The loading during compression is described using a simplified hyperfoam strain-energy function that effectively captures the nonlinear response of compressible polymer foams. For the unloading path, the model incorporates a scalar damage parameter controlled by three key variables: maximum damage, a damage evolution rate, and a transition parameter. Experimental validation confirms the model’s accuracy in predicting the mechanical response of polystyrene foams, including inelastic phenomena. This precision is supported by coefficient of determination R2 values close to unity when comparing the model’s predictions with experimental data. Thus, the proposed model provides a practical tool for analyzing the compressive stress response in polystyrene foams.
Theoretical and Applied Mechanics Letters 16 (2026) 100638.
doi: 10.1016/j.taml.2025.100638
Abstract:
This study tested the dynamic mechanical properties of seven commonly used backing plate materials and conducted ballistic experiments on their corresponding ceramic composite armor. The distribution of projectile fragments was quantitatively analyzed via the Rosin–Rammler model to assess ballistic outcomes. The results indicated that as the dynamic yield strength of the backing plates increased, the degree of projectile fragmentation increased, whereas the extent of plastic deformation decreased. A model of ceramic composite armor was established to analyze the propagation of one-dimensional stress waves within the armor. Research has shown that when the backing plates are in an elastic state, the intensity of stress waves in the ceramic significantly increases, but in a plastic state, most stress waves dissipate within the backing plates, resulting in weaker stress waves in the ceramic. Numerical simulations further quantified the impact of the plastic modulus of the backing plates on armor performance. Maintaining constant strain energy while increasing the plastic modulus improved the stress state at the ceramic back, shifting from tensile to compressive wave dominance, thus enhancing the overall ballistic resistance of the armor. A high sound speed in the backing plates helps optimize the stress state within the armor, thereby enhancing its ballistic performance.
This study tested the dynamic mechanical properties of seven commonly used backing plate materials and conducted ballistic experiments on their corresponding ceramic composite armor. The distribution of projectile fragments was quantitatively analyzed via the Rosin–Rammler model to assess ballistic outcomes. The results indicated that as the dynamic yield strength of the backing plates increased, the degree of projectile fragmentation increased, whereas the extent of plastic deformation decreased. A model of ceramic composite armor was established to analyze the propagation of one-dimensional stress waves within the armor. Research has shown that when the backing plates are in an elastic state, the intensity of stress waves in the ceramic significantly increases, but in a plastic state, most stress waves dissipate within the backing plates, resulting in weaker stress waves in the ceramic. Numerical simulations further quantified the impact of the plastic modulus of the backing plates on armor performance. Maintaining constant strain energy while increasing the plastic modulus improved the stress state at the ceramic back, shifting from tensile to compressive wave dominance, thus enhancing the overall ballistic resistance of the armor. A high sound speed in the backing plates helps optimize the stress state within the armor, thereby enhancing its ballistic performance.
Theoretical and Applied Mechanics Letters 16 (2026) 100639.
doi: 10.1016/j.taml.2025.100639
Abstract:
Data assimilation algorithms have been demonstrated to increase the accuracy of predictions in airfoil flow fields. However, slight changes in airfoil geometry and Reynolds number (Re) variations could lead to differences in aerodynamic characteristics and stall behavior, consequently affecting assimilation outcomes. Hence, this research uses the ensemble Kalman filter (EnKF) algorithm. The aerodynamic characteristics of two wind turbine airfoils obtained through wind tunnel experiments were investigated under varying degrees of stall by recalibrating the constants in the (S-A) model. The impacts of the airfoil thickness, Re variation, and Gurney flap installation on the assimilation results were subsequently examined. Verifying the applicability of the constants obtained via data assimilation under varying conditions might offer opportunities to reduce the demand for computational resources. The assimilation results indicate that at a Re on the order of magnitude of 105, the original model tends to delay flow separation as the Re increases. Consequently, the recalibrated constant Cb1 generally decreases with increasing Re. Despite belonging to the same airfoil family, discrepancies in the flow separation behavior predicted by the original model resulted in variations in the recalibrated constants. The constants derived from the thinner airfoil induce premature flow separation in the thicker YA-30 airfoil under stall conditions. When assimilated constants are applied to flow field calculations under analogous stall conditions, constants from another condition may demonstrate an optimization effect and substitute the self-assimilated constants, provided that simulations using default constants for both conditions consistently exhibit an experimental separation trend. However, practical implementation requires caution due to the risk of overadjustment.
Data assimilation algorithms have been demonstrated to increase the accuracy of predictions in airfoil flow fields. However, slight changes in airfoil geometry and Reynolds number (Re) variations could lead to differences in aerodynamic characteristics and stall behavior, consequently affecting assimilation outcomes. Hence, this research uses the ensemble Kalman filter (EnKF) algorithm. The aerodynamic characteristics of two wind turbine airfoils obtained through wind tunnel experiments were investigated under varying degrees of stall by recalibrating the constants in the (S-A) model. The impacts of the airfoil thickness, Re variation, and Gurney flap installation on the assimilation results were subsequently examined. Verifying the applicability of the constants obtained via data assimilation under varying conditions might offer opportunities to reduce the demand for computational resources. The assimilation results indicate that at a Re on the order of magnitude of 105, the original model tends to delay flow separation as the Re increases. Consequently, the recalibrated constant Cb1 generally decreases with increasing Re. Despite belonging to the same airfoil family, discrepancies in the flow separation behavior predicted by the original model resulted in variations in the recalibrated constants. The constants derived from the thinner airfoil induce premature flow separation in the thicker YA-30 airfoil under stall conditions. When assimilated constants are applied to flow field calculations under analogous stall conditions, constants from another condition may demonstrate an optimization effect and substitute the self-assimilated constants, provided that simulations using default constants for both conditions consistently exhibit an experimental separation trend. However, practical implementation requires caution due to the risk of overadjustment.
Theoretical and Applied Mechanics Letters 16 (2026) 100640.
doi: 10.1016/j.taml.2025.100640
Abstract:
High-fidelity strain measurements of plate and shell structures are crucial for elucidating failure mechanisms and deformation evolution. These data provide the basis for quantitative damage detection, design optimization, and structural health monitoring. However, laboratory constraints often preclude the acquisition of high-resolution full-field strains, limiting observations to a sparse set of discrete points. Reconstructing complete strain fields from these sparse measurements has therefore become a pressing challenge, for which few effective solutions exist. Motivated by the spatial correlations exhibited under blast loading, we develop a position- and physics-aware graph neural network (PPA-GNN) to recover transient strain fields in plate structures subjected to explosive impacts. The model employs graph-based message passing to encode both spatial topology and governing physical constraints among sensor nodes, markedly improving reconstruction fidelity. To cope with severe data sparsity in practice, we further devise a curriculum-learning schedule that gradually transitions training from dense to extremely sparse sampling, thereby enhancing robustness. The experimental results indicate that the PPA-GNN achieves an R2 value of 0.903 when only eight observation points are used, thereby demonstrating its capability for reliable full-field reconstruction under minimal sensing conditions.
High-fidelity strain measurements of plate and shell structures are crucial for elucidating failure mechanisms and deformation evolution. These data provide the basis for quantitative damage detection, design optimization, and structural health monitoring. However, laboratory constraints often preclude the acquisition of high-resolution full-field strains, limiting observations to a sparse set of discrete points. Reconstructing complete strain fields from these sparse measurements has therefore become a pressing challenge, for which few effective solutions exist. Motivated by the spatial correlations exhibited under blast loading, we develop a position- and physics-aware graph neural network (PPA-GNN) to recover transient strain fields in plate structures subjected to explosive impacts. The model employs graph-based message passing to encode both spatial topology and governing physical constraints among sensor nodes, markedly improving reconstruction fidelity. To cope with severe data sparsity in practice, we further devise a curriculum-learning schedule that gradually transitions training from dense to extremely sparse sampling, thereby enhancing robustness. The experimental results indicate that the PPA-GNN achieves an R2 value of 0.903 when only eight observation points are used, thereby demonstrating its capability for reliable full-field reconstruction under minimal sensing conditions.
Theoretical and Applied Mechanics Letters 16 (2026) 100641.
doi: 10.1016/j.taml.2025.100641
Abstract:
This work investigates the bidirectional relationship between contact mechanics and frictional wear behavior in bilateral constrained sliding contact. An internal state variable representing the contact surface condition is incorporated into the Coulomb friction law to account for wear phenomena. A contact detection method has been constructed to identify the positional relationship between two elements during contact, leveraging vector-related features of the vertices on the contact area between the slideway and the slider. A bipotential function for rigid bilateral constraints is formulated by introducing a stability factor. Combining the potential-Coulomb contact force model, a numerical algorithm is developed for variable friction contact problems on the basis of cumulative frictional dissipation and is initially implemented for rigid body bilateral contact problems. The algorithm is subsequently applied to bilateral constraint analysis in a sliding mechanism under both constant and variable friction conditions, and the influences of the wear and contact clearance factors are studied. The numerical results demonstrate consistency with energy conservation principles and dynamic laws, validating the effectiveness of the proposed algorithm. This work extends the applicability of the bipotential function approach and provides a theoretical foundation and analytical tools for optimizing bilateral nonideal contact structures and predicting equipment service life.
This work investigates the bidirectional relationship between contact mechanics and frictional wear behavior in bilateral constrained sliding contact. An internal state variable representing the contact surface condition is incorporated into the Coulomb friction law to account for wear phenomena. A contact detection method has been constructed to identify the positional relationship between two elements during contact, leveraging vector-related features of the vertices on the contact area between the slideway and the slider. A bipotential function for rigid bilateral constraints is formulated by introducing a stability factor. Combining the potential-Coulomb contact force model, a numerical algorithm is developed for variable friction contact problems on the basis of cumulative frictional dissipation and is initially implemented for rigid body bilateral contact problems. The algorithm is subsequently applied to bilateral constraint analysis in a sliding mechanism under both constant and variable friction conditions, and the influences of the wear and contact clearance factors are studied. The numerical results demonstrate consistency with energy conservation principles and dynamic laws, validating the effectiveness of the proposed algorithm. This work extends the applicability of the bipotential function approach and provides a theoretical foundation and analytical tools for optimizing bilateral nonideal contact structures and predicting equipment service life.
Theoretical and Applied Mechanics Letters 16 (2026) 100642.
doi: 10.1016/j.taml.2025.100642
Abstract:
This study presents a theoretical framework for analyzing a magnetically coupled multi-stable piezoelectric energy harvesting (PEH) system, comparing bistable and tristable configurations under initial perturbations. Through static bifurcation analysis, extended averaging, and numerical simulations, we reveal how nonlinear dynamics such as saddle-node bifurcations, chaos, and fractal basins of attraction (BAs) collectively influence efficiency. A magnetic coordination mechanism enables controlled switching between bistable and tristable potentials by adjusting the magnet spacing and vertical separation, challenging the conventional superiority of tristable designs. Specifically, the bistable system outperforms at low excitation amplitudes because of lower interwell thresholds, whereas the tristable setup excels only near trivial equilibria or within a moderate high-amplitude range. In an extreme-amplitude environment, the global attractive chaotic response that appears in the bistable system enhances the efficacy of such a system, demonstrating that chaos can benefit energy collection. This work establishes an excitation-amplitude-dependent selection principle for PEH designs and highlights the critical yet overlooked role of initial conditions. The observed fragile BAs and hidden/rare attractors provide new perspectives for enhancing system reliability.
This study presents a theoretical framework for analyzing a magnetically coupled multi-stable piezoelectric energy harvesting (PEH) system, comparing bistable and tristable configurations under initial perturbations. Through static bifurcation analysis, extended averaging, and numerical simulations, we reveal how nonlinear dynamics such as saddle-node bifurcations, chaos, and fractal basins of attraction (BAs) collectively influence efficiency. A magnetic coordination mechanism enables controlled switching between bistable and tristable potentials by adjusting the magnet spacing and vertical separation, challenging the conventional superiority of tristable designs. Specifically, the bistable system outperforms at low excitation amplitudes because of lower interwell thresholds, whereas the tristable setup excels only near trivial equilibria or within a moderate high-amplitude range. In an extreme-amplitude environment, the global attractive chaotic response that appears in the bistable system enhances the efficacy of such a system, demonstrating that chaos can benefit energy collection. This work establishes an excitation-amplitude-dependent selection principle for PEH designs and highlights the critical yet overlooked role of initial conditions. The observed fragile BAs and hidden/rare attractors provide new perspectives for enhancing system reliability.
Theoretical and Applied Mechanics Letters 16 (2026) 100644.
doi: 10.1016/j.taml.2025.100644
Abstract:
Metallic protective structures (e.g., beams and plates) are widely used against impact and blast loadings. Their precise dynamic responses are critical for design and service, especially when unintended preloading or prestress caused by accidental deformation is present. In this study, the effects of prestress on the structural deformation and springback behaviors of a fully clamped metallic beam subjected to a subsequent impact load are systematically investigated. A combined research approach, consisting of analytical modeling constructed by a simplified string-hinge model (SSHM) that accounts for the roles of structural hinge and string components as well as double-solver coupling numerical simulation incorporating implicit and explicit solvers simultaneously, is employed, which is validated against existing experimental results. The influence of material strain hardening is considered. The presence of prestress can improve the impact resistance of a beam by reducing its peak deflection and increasing the structural springback of the beam, owing mainly to altered beam geometries and, initially, the stress state as the beam is deformed. Using the analytical modeling of the SSHM, the roles of the components of the hinge and string under various loading scenarios are subsequently delineated, particularly in terms of the development process of the mechanical performance of each component within the out-of-plane deformation and springback stages. During the deformation process of the impacted target, the roles of the bending moment and membrane force vary with increasing midspan deflection. These roles also change when the pretension intensity is increased.
Metallic protective structures (e.g., beams and plates) are widely used against impact and blast loadings. Their precise dynamic responses are critical for design and service, especially when unintended preloading or prestress caused by accidental deformation is present. In this study, the effects of prestress on the structural deformation and springback behaviors of a fully clamped metallic beam subjected to a subsequent impact load are systematically investigated. A combined research approach, consisting of analytical modeling constructed by a simplified string-hinge model (SSHM) that accounts for the roles of structural hinge and string components as well as double-solver coupling numerical simulation incorporating implicit and explicit solvers simultaneously, is employed, which is validated against existing experimental results. The influence of material strain hardening is considered. The presence of prestress can improve the impact resistance of a beam by reducing its peak deflection and increasing the structural springback of the beam, owing mainly to altered beam geometries and, initially, the stress state as the beam is deformed. Using the analytical modeling of the SSHM, the roles of the components of the hinge and string under various loading scenarios are subsequently delineated, particularly in terms of the development process of the mechanical performance of each component within the out-of-plane deformation and springback stages. During the deformation process of the impacted target, the roles of the bending moment and membrane force vary with increasing midspan deflection. These roles also change when the pretension intensity is increased.
Submit a Paper
Subscription
News
MORE+
Call for Papers
MORE+
- Crossing-Mechanics Driven by Big Data
- Machine learning in the fluid mechanics research of wind energy
- Mechanics of Origami/Kirigami structures and metamaterials
- New insights and perspectives on impact biomechanics for human tissues: from injury prevention, protection to protective equipment
- Environmental Mechanics for Extreme Natural Events
