Abstract REBa 2 Cu 3 O 7− δ (REBCO, RE = rare earth) superconducting tapes exhibit broad application prospects in high-field superconducting magnets. However, limited by their uniform preparation length, connecting joints are inevitable in the magnets. Conventionally, the specific resistivity of the most used solder joints is above 20 nΩ·cm 2 @77 K and the concomitant dissipation heat and stress concentration become the primary factors causing the instability of the magnets. In this paper, a novel process is proposed to fabricate non-superconducting joints by electroplating nanocrystalline copper on the surface of REBCO tapes and bonding through grain growth. Under a new low-temperature (140 °C) and low-pressure (50 MPa) bonding process, flexible joints with a specific resistivity as low as the level of 5.87 ± 0.36 nΩ·cm 2 @77 K are fabricated. To the best of our knowledge, the specific resistivity has reached the lowest value among non-superconducting joints. Microscopic experimental characterizations, phase-field and molecular dynamics simulations reveal that in the synergistic environment involving both pressure and temperature gradient conditions, the temperature gradient dominates grain growth along the heat flow direction, resulting in the elimination of the initial bonding interface, accompanied by flexibility and debonding strength up to 2 GPa. These findings in this work not only provide key technical support for development of the joints with low resistivity and high strength but also offer a reference for the optimization of bonding interfaces in chip stacking and packaging.

The T-A formulation, which couples the magnetic vector potential A and the current vector potential T, has become one of the dominant models for the electromagnetic modeling of high-temperature superconducting (HTS) structures. Due to the limitation of the mixed formulation, the discretization of the T-A formulation needs to be performed carefully to prevent spurious numerical oscillations. For this purpose, the second-order Lagrangian elements are employed for the magnetic vector potential A, and the linear elements for the current vector potential T. Nevertheless, the higher-order elements increase the degrees of freedom and restrict the computational efficiency. In this paper, a reduced-order T-A formulation is proposed based on mesh misalignment to eliminate the oscillation phenomenon and improve the computational efficiency. The mesh misalignment ensures that the electromagnetic energy is calculated at the consistent node without additional interpolation by the product of work-conjugate quantities (the magnetic vector potential A and the current density J). In this way, the linear elements are applied for the magnetic vector potential A and the current vector potential T. Therefore, the spurious numerical oscillations disappear in the reduced-order T-A formulation. And the degrees of freedom are significantly reduced. The reduced-order T-A formulation could significantly improve the computational efficiency for electromagnetic modeling of large-scale superconducting systems, especially for the three-dimensional HTS structures.

The electromagnetic computation of superconductors involves highly nonlinear current-voltage characteristics (i. e., the power law relationship between Electric field E and Current density J) and multiphysics coupling between temperature and magnetic fields, which pose challenges to numerical accuracy and convergence. This study presents a coupled electromagnetic-thermal-fluid model based on the lattice Boltzmann method (LBM) to analyze the multiphysics behavior of high-temperature superconductors. The governing equations of the electromagnetic field, the heat conduction equation of the temperature field, and the Navier-Stokes (NS) equations of the flow field are solved in this model. Numerical simulations of the pulsed field magnetization process with this model demonstrate that LBM shows good convergence and computational efficiency compared to finite element method (FEM). Additionally, the model is extended to simulate boiling phenomena in liquid helium triggered by heat dissipation from superconductors, capturing the transition processes among natural convection, nucleate boiling, and film boiling regimes. The results highlight the potential of LBM for efficient multiphysics simulations in superconducting applications.

Due to the opacity of conductive solids and the strong randomness and complexity of contact interfaces, the stress distribution at the interface has long remained "not directly observable," making it a key challenge in the evaluation of engineering structures. To address the dual challenges that stress cannot be measured directly and that interfaces are located inside opaque solids, an electrical method for interfacial stress measurement is proposed. The method exploits the stress sensitivity of electrical signals and the penetrability of electric current in conductive media. It enables the coordinated measurement of internal structural features and stress states in conductive solids. First, a governing equation for the electric potential field is established based on Ohm's law and the current continuity equation. The response characteristics of the electric field are then analyzed to obtain the distribution pattern of sensitivity along the depth direction. On this basis, the relationship between electrode spacing and probing depth is constructed, thereby revealing the current transport mechanism in conductive structures. On this basis, a distributed multi-electrode electrical measurement method is proposed to achieve accurate characterization of internal structural features in conductive solids. Based on this method, a matrix "resistivity-stress" correlation model and an interface "contact resistance-contact stress" correlation model are further established. The accuracy of the models is verified by comparison with existing experimental data. The results show that the model predictions agree well with the measured data. The electrical measurement method proposed in this paper overcomes two major challenges. One is that interfacial stress cannot be measured directly. The other is that interfaces are located inside opaque solids. This method promotes the development of interfacial stress measurement methods.

The sealing performance of flared aviation hydraulic pipe joints directly determines whether the aircraft can operate safely. Accurately analyzing the contact forces at the joints and revealing the mechanism through which they affect the sealing performance are essential for resolving leakage failures. In this study, a new leakage prediction model for flared aviation hydraulic pipe joints is developed based on a contact mechanics model that accounts for both normal and tangential forces acting on the sealing interface. The average separation of the interface was redefined from variations in the void volume of rough surfaces, and its relationship with the leakage rate was derived through contact deformation, enabling prediction of the joint’s leakage behavior. The results demonstrate that the proposed model considers the impact of tangential forces on interfacial sealing, improving leakage rate prediction accuracy by 28.5%. This improvement is mainly attributed to accounting for the influence of tangential forces on the average separation of the interface and the real contact area. This work provides insight into the leakage mechanism at metal-metal sealing interfaces and offers theoretical guidance for analyzing sealing performance and optimizing assembly process parameters of hydraulic pipe joints.

The parallel-wound no-insulation (PWNI) high temperature superconducting (HTS) coils have garnered significant research interest due to their low time-delay characteristics. This study develops an electromagnetic-mechanical coupled model for the PWNI HTS coil, and its accuracy is confirmed through high magnetic field experiments. Numerical results demonstrate that while non-uniform current distribution among turns aggravates mechanical deformation, this effect can be effectively mitigated by maintaining stable operation of post-excitation. Furthermore, the separation behavior (comprising both loop-to-loop and turn-to-turn) exhibits distinct and evolving spatio-temporal characteristics across different operational stages. This separation behavior alters the radial contact resistance, which significantly influences the radial current distribution while has a negligible impact on the azimuthal current. Finally, analysis of the loss characteristics of PWNI coil indicates that loop-to-loop Joule heat loss predominates in the PWNI coil. The background field magnetization process dissipates more energy than the charging phase due to its longer duration. Under high magnetic fields, magnetization losses are primarily concentrated in the upper section of the coil, and the joule heating loss diminishes as a result of increased radial contact resistance.

Abstract The bolted connection structure is used in fields such as mechanical equipment, aerospace, and civil engineering. Its preload state directly affects the load-bearing capacity, service reliability, and safety of the connection structure. The existing methods for measuring and evaluating bolt preload mostly focus on the bolt body as the research object, mainly reflecting the variation law of preload through parameters such as bolt length change, strain response, or axial elongation. However, the preload is closely related to the contact state of the connection interface. Especially, changes in the porosity of the connection interface can alter the true contact area and local stress distribution of the interface, thereby affecting the overall mechanical properties of the connection structure. A new method for characterizing the contact state of bolts based on contact mechanics from the perspective of interface porosity and establishing a preload measurement model based on interface porosity is proposed. This method not only enables effective measurement of changes in bolt preload but also further characterizes the contact state of the connection interface, revealing the relationship between interface porosity, real contact area, and interface contact pressure. The results indicate that the measurement error of preload force is less than 10%, and it simultaneously analyzed the contact state of the connection interface. This study expands the analysis object of preload from the bolt body to the connection interface, providing a new research method for health monitoring, reliability evaluation, and anticrushing design of bolt connection structures under complex service conditions.

Differently from the continuum medium, multilayered structures are discontinuous systems, which consist of a series of plates or shells stacked on each other. The global kinematic feature of the multilayered structure is determined by the local kinematics of its monolayers and the interfacial movement between them. At the interface, contact pressure works in the normal direction, and friction works in the tangential direction, which remarkably impacts the mechanical responses of multilayered structures. The multilayered structures have the following kinematic characteristics: interfacial slip is kinematically permissible and the contact gap can be negligible during deformation. Based on these features, the midplane displacements of each shell layer can be constructed as a continuous field. Layer-to-layer interactions are treated as internal forces, and the Coulomb friction law is incorporated as a material constitutive relationship. In kinematics, interfacial slip is taken into account in the global strain-displacement relationship, which leads to a correction term in the governing equation according to the dual relationship. In dynamics, the principle of minimum potential energy is utilized to derive the governing equation, with friction being accounted for through the mechanism of energy dissipation. Then, a continuum theory for multilayered structures is proposed in this paper and validated by comparisons with the discrete contact model and experiments. The proposed model is further extended to the mechanical study of high-temperature superconducting (HTS) magnets. The complexity of HTS magnets stems from the large number of contacts and the corresponding contact nonlinearity, which gives rise to computational inefficiencies and convergence problems. The proposed model could address these challenges and facilitate the mechanical analysis of HTS magnets.

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.

The contact deformation and buckling of elastic rods against rigid surfaces represent a prevalent phenomenon in applications such as oil drilling, arterial stents, and energy harvesting. This has attracted widespread attention from researchers. In this paper, the deformation and buckling behaviors of a circular arch subject to compression by a rigid plate are investigated with a planar elastic rod model that incorporates tension, shearing, and bending. In comparison with the existing models that solely consider the bending energy, the deflection curve, the internal force distribution, and the critical load of the present model show good agreement with the finite element results. Through the dimensional analysis and order-of-magnitude estimation, we examine the factors influencing the critical load. The study reveals that the semi-central angle of the arch has the most significant effect. The dimensionless geometric parameter describing arch slenderness becomes prominent when the semi-central angle is less than 30°, while Poisson’s ratio and the cross-sectional shear correction factor exhibit negligible influence. Furthermore, the variation in the proportions of strain energy components during critical buckling is presented with respect to the semi-central angle and the geometric parameter, thereby delineating the applicable ranges of both the original model (OM) and the modified model (MM).

Multilevel helical structures (MHSs) have been extensively employed in engineering and biomimetic applications due to outstanding global load-bearing capacity and local contact mechanical performance. However, the fundamental scaling relationship between macroscopic geometry and local contact forces in MHSs has remained inadequately elucidated, which severely limits the quantitative prediction of contact-induced behaviors (e.g., fretting wear and contact fatigue). To address this challenge, a general theoretical model is established to investigate the scaling-law behavior of discrete contact forces. By introducing modified internal force/moment terms that account for the characteristic transposition contact distance into the equilibrium equations of thin rod theory, explicit expressions for discrete contact forces of MHSs with arbitrary winding patterns are derived. Furthermore, a concise and unified scaling law is established through order-of-magnitude analysis, demonstrating that the dimensionless point contact parameter Q follows a -1-power exponential law relationship with the construction parameter m, defined as the ratio of the winding angles between helices of adjacent orders. The validity of this scaling relationship is confirmed through contact resistance experiments and finite element analysis (FEA). Based on the establishing scaling law, the intrinsic relationship between the topological entanglement number and the contact force is further revealed. The proposed scaling law offers critical theoretical guidance for MHS geometric parameters to mitigate friction-induced damage, reduce fretting wear, and enhance the tribological performance and service life of engineering components relying on hierarchical helical structures.

Normal and tangential forces coexist between rough surfaces in engineering components under most operating conditions.Accurate measurement of contact forces(both normal and tangential forces)on rough surfaces is critical for the safety and stability of engineering equipment,as interfaces are typically discontinuous regions within mechanical systems.However,existing contact mechanics and electrical contact models mostly neglect tangential force effects,hindering their application to shearing behavior research and precluding the development of a contact force measurement methodology applicable to simultaneous normal and tangential force quantification.Inspired by the yield criterion for material damage,a contact mechanics model was developed that simultaneously accounts for the effects of normal and tangential forces.Then,a new principle of contact force measurement is developed by correlating the contact resistance with the real contact area,which enables the simultaneous measurement of normal and tangential forces between rough surfaces based on the single contact resistance under steady-state contact conditions.By proposing a"static friction surface",the static and dynamic friction stage is effectively differentiated,and the reasons for the sudden drop in friction force and the sudden increase in contact resistance during the static and dynamic transition stages are given.This work proposes a novel explanation for the friction mechanism in terms of mechanical deformation and electrical resistance changes.

The magnetohydrodynamic (MHD) boundary-layer flow of an upper-convected Maxwell (UCM) fluid is investigated using asymptotic analysis. The governing nonlinear partial differential equations are first reduced to ordinary differential equations via boundary-layer approximations and similarity transformations. An asymptotic solution satisfying the prescribed boundary conditions is then constructed using the homotopy renormalization method based on Taylor expansion. The analytical results show that the Hartmann number modifies the velocity distribution via the Lorentz force, introducing electromagnetic damping into the momentum balance and affecting the boundary-layer structure. Increasing the Deborah number enhances the elastic contribution from the upper-convected Maxwell model, influencing near-wall shear behavior and nonlinear coupling. In the asymptotic limit of vanishing Deborah number, the governing equation reduces to the classical Newtonian MHD boundary-layer formulation. To validate our analytical results, we develop a numerical scheme based on interpolation wavelet collocation to solve the original partial differential equations directly. Comparisons reveal excellent agreement between the asymptotic and numerical solutions throughout the flow domain. The parameter ranges correspond to moderate magnetic interaction and weak-to-moderate viscoelastic effects relevant to polymer extrusion, electrically conducting coating flows, and liquid-metal cooling under magnetic fields. The asymptotic expressions provide insight into the coupled effects of inertia, elasticity, and electromagnetic forces.

Critical components in aerospace, nuclear power, and advanced manufacturing operate under high-temperature friction, where oxidation forms an interfacial film that significantly alters friction and wear behavior. The oxide scale undergoes dynamic competition between temperature-driven growth and continuous removal by sliding, resulting in complex and poorly understood kinetics. However, a unified kinetic description that couples oxidation growth with stress effects, thermal softening, and sliding-induced removal under high-temperature wear remains limited. This paper presents a theoretical model that explains the growth of oxide films of single-phase (Dy0.2Ho0.2Er0.2Tm0.2Lu0.2)B12 (HEB12) ceramics under high-temperature wear conditions. It forecasts the dynamics of film formation and elucidates how the film impacts wear behavior. We conducted a comprehensive analysis of how temperature, pressure, and sliding speed govern oxide-film growth and wear behavior. This work clarifies the mechanisms underlying high-temperature friction and wear and provides a theoretical foundation for their interpretation. Additionally, it offers practical guidance for the design and fabrication of tribological components intended for extreme service conditions.

A fourth-order conservative adaptive multiresolution average-interpolating wavelet upwind scheme is proposed for compressible flows governed by hyperbolic conservation laws. A family of asymmetric average-interpolating wavelets with upwind properties is constructed for conservative finite volume discretization, while symmetric average-interpolating wavelets are employed for multiresolution decomposition and reconstruction of physical variables in the adaptive procedure. Since both the conservative discretization and the adaptive multiresolution representation are constructed from cell-average quantities, the proposed scheme preserves strict conservation during both numerical evolution and adaptive cell redistribution. Unlike hybrid adaptive wavelet methods that use wavelets mainly for data compression and mesh adaptation, the present adaptive wavelet upwind scheme utilizes average-interpolating wavelet multiresolution approximation to reconstruct the interface values directly for numerical flux evaluation, thereby avoiding additional ghost-cell marking and reconstruction near coarse–fine mesh interfaces. The boundary variation diminishing reconstruction is incorporated at the finest resolution level to achieve non-oscillatory shock-capturing capability. Numerical tests demonstrate that the proposed scheme achieves the expected fourth-order accuracy, maintains conservation errors close to machine precision, and controls numerical errors around the prescribed threshold. The proposed method also sharply captures shock waves and contact discontinuities without spurious oscillations and resolves multiscale smooth structures through a sparse adaptive representation. These results indicate that the proposed scheme provides an efficient, conservative, and reliable approach for high-resolution simulations of compressible flows.

Hierarchical chiral helical structures integrate superior load-bearing capacity with flexible deformability, and their unique tension-torsion coupling effect provides a core foundation for the design of programmable metamaterials, twisted soft actuators and bio-inspired composites. Focusing on two key mechanical indicators: structural energy dissipation capacity and interfacial contact stress distribution, this work establishes universal governing laws of structural chirality and geometric parameters for regulating the mechanical performance of hierarchical chiral helical systems. A global-local homogenization model is proposed to derive the explicit expressions for the stiffness components of hierarchical chiral helical structures based on a linearization approach. Notably, a coupling-decoupling coefficient is defined based on the derived stiffness components as a key control parameter, which reveals the regulatory mechanism of chirality on global tension-torsion coupling behavior. The validity and universality of the proposed model are verified by comparing with experimental tests and finite element simulations. The proposed model can not only accurately predict the global tension-torsion coupling behaviors, but also quantitatively characterize the local contact stress field. Furthermore, the competitive contributions of multiple strain energy components are clarified under combined loading conditions. Based on the tension-torsion decoupling characteristic, a type of mechanically programmable metamaterial system is further designed to realize the fitting of complex curves and the efficient separation of tension-torsion loads. This research offers predictive design rules for energy dissipation and interfacial contact stress of hierarchical chiral helical structures, which provides an efficient quantitative tool of complex mechanical responses for hierarchical chiral systems from 1D biomimetic filaments, 2D helical sub-cables to 3D architected metamaterials.

The contact behavior of curved surfaces is critical to the structural performance of applications in fields such as aerospace and flexible electronics. However, the significant curvature variations resulting from the geometric complexity of curved structures make it difficult for traditional models to accurately characterize interfacial contact force and electrical conductivity. To address this challenge, this study incorporates the effects of curved configurations and establishes a quantitative relationship between normal contact force and interfacial contact resistance. To validate the effectiveness of the model, experimental measurements were conducted on copper alloy coil structures. The results showed that the predicted electrical contact resistance is in good agreement with the experimental data. Compared with planar surface contact models, the curved surface contact model developed in this study improved the prediction accuracy of electrical contact resistance, demonstrating its adaptability and precision in describing the electro-mechanical behavior of curved structures. The findings of this study provide a new theoretical approach and engineering reference for predicting and evaluating interfacial contact performance in structures with curved configurations.

For type-Ⅱ superconductors, the critical state model assumes that the current density does not exceed the critical threshold, and the electric field remains zero below this threshold. Physically, this behavior relates to the flux pinning mechanism, which restricts the motion of magnetic flux through the pinning force. At the pinning point, the vortex is captured, and the motion of the flux is suppressed until a critical threshold is reached. In mathematics, the above behavior can be characterized by an inequality constraint condition, and the theory of variational inequalities can be applied. Nevertheless, a versatile and efficient numerical tool based on the finite element method is still required to describe the critical state model. This paper aims to characterize the features of the critical state model from the perspective of the material constitutive relationship. The critical state model can be characterized by the principle of maximum dissipation, which states that the dissipation in the superconductor reaches a maximum during a dissipative process. Then, the flow rule and Kuhn-Tucker complementary condition are given, which describe the material constitutive relationship of the critical state model. In numerical implementation, the A formulation is adopted to numerically discretize Maxwell equations, and the material constitutive relationship is regularized to ease numerical implementation. Meanwhile, the numerical oscillations in the large gradient region are eliminated by changing the discretization scheme. In this way, an efficient and universal model is presented to calculate the critical state of superconductors.

The threaded contact interface is difficult to detect because of its complexity and internal contact characteristics, such as the squeezing contact between the thread of a shear bolt and the hole wall. How to non-destructively detect the contact force of the thread contact interface is the key issue to solve the problem of thread damage detection, which is highly important for the normal use of bolts. This paper aims to explore a new electrical measurement method that measures the contact force state between the thread of a shear bolt and the hole wall by measuring the squeezing contact electrical signal. However, owing to the influence of the helical structure, the contact force between the thread and the hole wall is very complex and includes both normal and shear forces. In this paper, contact forces are measured by measuring electrical signals under pressure. By combining the electrical contact model, a thread/hole wall electro-mechanical contact model is established, forming the principle of contact force measurement. Compared with traditional contact mechanics theory, this paper considers the influence of the helical configuration on the interface contact behavior, providing a theoretical reference for predicting bolt thread failure. The accuracy of the model was verified through experiments, with a maximum error of less than 10%. Further research and analysis were conducted on the parameters of the electro-mechanical contact model and actual engineering. This model can be used to measure the normal contact force between the shear thread and the hole wall, laying the foundation for detecting thread failure.

As a critical component of the International Thermonuclear Experimental Reactor (ITER), the complex stress state of superconducting wires within Cable-in-Conduit Conductors (CICC) significantly impacts overall system performance. To address the high computational and economic costs associated with traditional numerical simulations and experiments, a multiscale numerical model is developed based on the asymptotic homogenization method (AHM) to study the macro global mechanical responses and micro stress states of CICC sub-cables. The numerical model incorporates macroscopic modeling while retaining the microscopic information from superconducting wires. Macroscopic strain data from the sub-cable are input into a representative volume element (RVE) to obtain the true microscopic stress distribution. The AHM framework's accuracy is validated by comparing the global mechanical responses, local contact forces, and micro stress distributions of sub-cables with results from direct numerical simulations (DNS), experiments and theoretical analysis. Compared to DNS, AHM-based numerical modeling reduces computational time cost by an order of magnitude while ensuring the validity of the calculation results. Furthermore, the axial load bearing capacity and lateral contact force of three representative superconducting sub-cables are evaluated, revealing that adjusting structural parameters of sub-cables can improve local contact forces while keeping von Mises stress of filament bundles change slightly, which enhances the global load-bearing and local contact performance. This work provides a valuable framework for efficient multiscale numerical modeling of CICC multilevel sub-cables containing thousands of composite wires.