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In this paper, the elastic wave band gap characteristics of two-dimensional hard-magnetic soft material phononic crystals (HmSM-PnCs) under the applied magnetic field are studied. Firstly, the relevant material parameters of hard-magnetic soft materials (HmSMs) are obtained by the experimental measurement. Then the finite element model of the programmable HmSM-PnCs is established to calculate its band structure under the applied magnetic field. The effects of some factors such as magnetic field, structure thickness, structure porosity, and magnetic anisotropy encoding mode on the band gap are given. The results show that the start and stop frequencies and band gap width can be tunable by changing the magnetic field. The magnetic anisotropy encoding mode has a remarkable effect on the number of band gaps and the critical magnetic field of band gaps. In addition, the effect of geometric size on PnC structure is also discussed. With the increase of the structure thickness, the start and stop frequencies of the band gap increase.

High-temperature superconductor (Re)Ba2Cu3O x (ReBCO) conductor on round core cable (CORC®) has a large current carrying capacity for high field magnets. Lorentz forces acting on CORC conductors, cause a reduction of the critical current, or even permanent degradation of their performance when exceeding critical values. Transverse compressive stress is one of the principal mechanical stresses when CORC cables are bundled to cable-in-conduit conductors (CICC) conductors capable of operating at currents up to 100 kA in magnetic fields of up to 20 T. In this research, a mechanical-electromagnetic model is developed to study the effect of transverse compressive loads on the electromagnetic performance of CORC cables. A mechanical transverse load on the cable is implemented to simulate the electromagnetic force. A comparison of numerical simulations with experiments for a three-layer CORC cable is first performed to validate the model’s reliability, with particular attention to critical current reduction during the transverse compression process. A novel feature of this paper is that the model developed can analyze both mechanical response under transverse compressive loads and electromagnetic performance under applied AC magnetic fields with low amplitudes. On this basis, the model investigates the effects of winding parameters on the axial strain and critical current reduction of the ReBCO layer in a single-layer CORC cable. The numerical analysis shows that increasing the winding angle can reduce the axial strain and critical current reduction of the ReBCO layer in the contact area. Subsequently, a detailed comparative study is carried out studying the axial strain of the ReBCO layer in the non-contact area with and without taking the winding core into account. In addition, a sudden increase in the magnetization loss is explained when the transverse compressive load reaches a certain level. Finally, a six-layer CORC cable’s electromagnetic analysis is performed, and each tape layer’s critical current reduction is investigated and discussed. The comparison of magnetization loss and current density between six- and single-layer CORC cables in the no-strain case is also given. This finite element model can guide optimizing a cable design for specific application conditions.

Superconducting Nb3Sn Rutherford cables can be used in the accelerator magnets above 10 T regions that cannot be reached with NbTi. These cables are composed of superconducting multifilamentary strands, interstitial epoxy, and insulation materials. To properly design the magnets made from these cables, it is essential to analyze their mechanical behavior. The prerequisite for this is the knowledge of the mechanical performance of Rutherford cables. In large magnets, these cables cannot be modeled with all details but effective properties and homogenization are typically required. In this work, an analytical model and numerical approach for predicting the effective mechanical properties of Rutherford cables are developed. The analytical model is established on a two-step homogenization and mechanical analysis for composite. The effective mechanical properties of the filament area and the transverse Young's modulus of the strand are first determined by means of utilizing the mechanical theory of the unit cell approach. The composite effective mechanical properties of the strand and interstitial epoxy are homogenized in the first step. The second step homogenization derives the effective mechanical properties of the strands epoxy composite and insulation layers. The numerical approach to determine the effective mechanical properties is based on the finite-element analysis. The developed methodologies are used to obtain the effective mechanical properties of two Nb3Sn Rutherford cables. The influence of the insulation thickness and modulus, the strand's modulus, is studied.

The Conductor on Round Core (CORC) wire coming under the category of High-Temperature Superconducting (HTS) wires is the promising type used in next-generation magnet-based applications, such as fusion, particle accelerator, magnetic resonance imaging (MRI). However, mechanical deformation due to cabling, winding, and operation of the magnets will degrade the performance of the HTS wires, which might cause severe problems in several aspects. The study of contact characteristics inside the superconducting wire is of considerable significance since they are essential parameters for the understanding of mechanical and electrical responses, indicators for optimizing the cable structure. It also contributes to the safe operation and feasibility of HTS magnets. In this paper, dynamic finite element simulations are applied to obtain the mechanical response of stretched CORC wires. The deformation and the contact stress of the inner tapes are presented. Engineering optimization is done by analyzing the results. © 2002-2011 IEEE.

Pressure drop of cable-in-conduit conductors (CICCs) cooled by a flow of liquid or supercritical helium is one of the key parameters for the design of large superconducting magnet systems, which determines the heat removal capability and the thermal stability. In this article, an analytical model for predicting the pressure drop in CICCs is developed based on an analogy to porous media with the equivalent geometry configuration. This new prediction model indicates that the pressure drop in CICCs is affected by the geometry parameters of cable and the physical properties of the liquid helium, such as void fraction, tortuosity, pore-throat ratio, hydraulic diameter, density, and viscosity of the liquid helium. To verify the validity of the pressure drop model proposed in this article, the predictions are compared with the experimental data, the results show that the predictions are in good agreement with the experimental data. Then, an analytical expression for predicting the friction factor is derived, the obtained expression is in good agreement with experimental data and is superior to the Katheder correlation at large Reynolds number. In addition, the effects of the major geometric parameters on pressure drop are analyzed, the results explain why the Katheder correlation can be used to predict the pressure drop of CICCs.

We established a three-dimensional (3D) multifilament finite element model for Bi-2212 round wire under axial load and analyzed its mechanical behavior. The model considered the initial thermal residual stress and damage of Bi-2212 superconducting filaments. The proposed model accurately predicted the axial mechanical behavior of strands. In addition, the characteristics of hysteresis loops in the stress–strain curves of Bi-2212 high-temperature superconducting (HTS) round wire under axial cyclic load were also obtained, agreeing well with experimental data. We constructed a 3D multifilament finite element model and 3D homogenized finite element model of a Bi-2212 HTS triplet. Both the results predicted by multifilament finite element model and homogenized model are close to the experimental data. The former gave more accurate stress distribution characteristics of strands than the latter. However, the homogenized model maybe more suitable for modeling of higher-level cables than the triplet model because of its lower computational cost.

The investigation of hysteresis induced self-biased magnetoelectric (ME) coupling in multiferroic nanostructured films is significant for self-biased nano-devices. In this paper, we propose a quasistatic hysteresis model for ME effect in multiferroic nanostructured films based on surface stress model and multi-field coupled hysteretic constitutive model. For an asymmetric structure consisting of different magnetostrictive phases, the flexural strain is considered in the theoretical model. It is revealed that ME coupling in ME composites with nano-scale thickness is significantly size-dependent below critical size, which is enhanced by surface effect. Self-biased ME hysteretic behavior can be observed by considering the hysteretic effect of magnetostrictive materials, resulting in a large ME voltage coefficient in absence of bias magnetic field. The self-biased ME voltage coefficient is affected by pre-stress and thermal variation due to the complex magneto-elastic-thermal coupling characteristics of constituent materials. The proposed model provides a method to analyze and evaluate the nonlinear ME coupling characteristics of self-biased nano-devices operating under extreme stress or temperature conditions.

Contact resistance is key for stable operation of electrical contact equipment, and can also be extensively applied. For Tokomak devices in fusion reactors, contact resistance of the superconductor magnet system strongly relates to the alternating current (AC) loss of the cable, the cable is assembled using a certain number of contacting superconducting tapes coated with copper layers on both sides. The contact resistance of a metal solid surface is affected by many factors. In this work, the contact resistance of copper surface samples was studied experimentally under variable normal cyclic load, temperature and number of contact surfaces. This is consistent with real-world working conditions, as the structure of superconducting cables can be changed, and such cables are used under cyclic electromagnetic forces in temperatures which range from room to working temperature. Experimental results showed that contact resistance decreased rapidly with an increase of load. Further, when temperature was varied from 77 to 373 K, the load&ndash, unload contact resistance lag decreased. When the number of contact surfaces was increased, contact resistance increased. Finally, a fitted formula describing the relationship between contact resistance and cyclic times, temperature and number of contact interfaces was determined. This formula can be used to predict variation trends of contact resistance in complex environments and provide more accurate contact resistance parameters for calculating the AC loss of superconducting cables.

The performance of a multi-layer composite superconducting tape depends on operating conditions, such as the applied field, temperature and stress. Therefore, accurate analysis of the electromagnetic-thermo-mechanical coupling behaviors of the high-temperature superconducting (HTS) cable is important to understanding the mechanism of interaction among different physical fields and the success of optimizing the design of the HTS cable structure. This paper develops a three-dimensional finite element model based on the twisted-stack slotted-core HTS cable structure for electro-thermo-mechanical analysis. Critical currents of a single multi-layer composite superconducting tape and the whole HTS cable structure are calculated. Profiles of the magnetic field, current density, temperature and stress are also obtained. It is found that the selection of tapes having higher critical current enhances the transport performance of the cable. Current densities are nonuniformly distributed in the stack. From the bottom to the top of the stack, the current density first increases and then decreases, in inverse relation to the magnetic field. Cooling with liquid helium improves the cable transport capacity. The temperature of the superconducting tapes is slightly higher than that of the aluminum core, but the stress in the aluminum core is greater than that in the superconducting tapes. The results imply that the transport capacity of the cable can be improved by selecting superconducting tapes with high critical current density and arranging them in stacks in a manner consistent with the electromagnetic field distribution. The model also explains the mechanism of interaction between different physical fields. It is a useful tool that clarifies the multiphysics coupling behaviors of an HTS cable with complex structure, and provides a theoretical reference for the design of novel HTS cable structures.

Both the pancake coiling and conductor on round core (CORC) cabling processes consist of winding second-generation high-temperature superconducting tape (REBCO) in a core. The contact behavior between the tape and the core during the winding process directly affects the critical current, cable flexibility, mechanical support and electrical contact resistance. Therefore, the winding process needs to be optimized to produce pancake coils and CORC cables with the desired electrical and mechanical properties. This paper comprehensively considers the role of the relaxation and Poisson effects. The theoretical model and the finite element model (FEM) for calculating the contact stress during the winding process are established, and a formula for the estimation of the contact force is proposed. The suitable winding pre-tension force, winding curvature radius of SCS2030 (2 mm width and 30 μ m substrate thickness) and SCS4050 (4 mm width and 50 μ m substrate thickness) of REBCO tapes are obtained and discussed by accounting for the relaxation effect and the critical current degradation limit. With consideration of the Poisson effect, the nonlinear contact behavior is investigated. In addition, the relaxation effect, Poisson effect and plasticity of the REBCO tape are taken into account in the FEM model. The results show that the axial strain in the REBCO layer during the winding process is related to the contact behavior. The greater the winding pre-tension force, the smaller the helical curvature radius, and the greater the contact force. The distribution of contact stress for several winding factors (winding pre-tension force, winding angle and the core radius) is divided into three contact types: the single-line contact, the double-line contact and the surface contact. The FEM model results are consistent with the theoretical evaluation and are more suitable for practical winding cases. This research is the basis for designing and optimizing pancake coils and CORC cables.

In this study, we investigate the nonlinear magnetoelectric (ME) response of a tri-layer ME laminate structure in a harmonic magnetic field. A coupling three dimensional (3D) finite element model of ME composite is built. Based on the Maxwell equations and a nonlinear magnetization relation proposed by Liu and Zheng, the inhomogeneous magnetic field distribution inside the layered ME composite are investigated by using the finite element method (FEM), moreover, the width of structure on magnetic field distribution and ME response are discussed in detail. Subsequently, the non-uniform distributions of stress, displacement, magnetic flux density and voltage are studied, and edge effect appears. Besides, the dynamic ME coefficient is also calculated and discussed. The results indicate that it’s necessary to consider the real distribution of the magnetic field in the calculating the nonlinear ME response. The geometric size affect the ME coefficient obviously, the ME coefficient considered the width effect is smaller than analytical result and more close to the experimental data. Through analysis the stress state of the structure, the result shows that both the normal stress and shear stress in the interface are large when the laminate structure under resonance, which may lead to the interfacial debonding.

We present a model for the variation of the upper critical field Hc2 with Sn content in A15-type Nb-Sn wires, within the Ginzburg-Landau-Abrikosov-Gor’kov (GLAG) theory frame. Hc2 at the vicinity of the critical temperature Tc is related quantitatively to the electrical resistivity ρ, specific heat capacity coefficient γ and Tc. Hc2 versus tin content is theoretically formulated within the GLAG theory, and generally reproduces the experiment results. As Sn content gradually approaches the stoichiometry, A15-type Nb-Sn undergoes a transition from the dirty limit to clean limit, split by the phase transformation boundary. The H-T phase boundary and pinning force show different behaviors in the cubic and tetragonal phase. We dipict the dependence of the composition gradient on the superconducting properties variation in the A15 layer, as well as the curved tail at vicinity of Hc2 in the Kramer plot of the Nb3Sn wire. This helps understanding of the inhomogeneous-composition inducing discrepancy between the results by the state-of-art scaling laws and experiments.

For improving harvesting ability and adjusting resonant frequency, magnetic energy harvesters using functionally graded composite cantilever are analyzed theoretically. Simultaneously, output voltage of the harvester composed of homogeneous materials is measured experimentally to verify the developed model. In the theoretical model, functionally graded properties with a power-law distribution along the thickness are considered for piezoelectric and substructure layers. Two types of harvesters are designed based on the surface material properties of piezoelectric bimorph. The outputs (electric current, voltage, power etc.) under closed-circuit condition with impedance are derived. When the impedance value tends to infinity, the model successfully reduces to the one for magnetic sensors under open-circuit condition. The influence of the driven frequency, power n and impedance value on output power is studied in detail. Some comparisons are made between two harvesters to select the one with superiority. Then, the influence of substructure's thickness is analyzed. Finally, two available methods are put forward to broaden the responsive frequency range. The numerical results show that the introduction of functionally graded materials can enhance the magneto-mechano-electric coupling effect of harvesters. Different optimal impedances values can be obtained under different frequencies and n values, with whom the best harvesting ability is achieved. Moreover, the resonant frequency of the cantilever is effectively tuned by altering parameters. For the harvester composed of homogeneous materials, the theoretical results agree well with experimental data.

In this paper, the magnetoelectric (ME) effect is investigated in two kinds of A-line shape Terfenol-D/PZT-5A structures by changing the position of the NdFeB permanent magnet. The experimental results show that both ME composite structures had multiple resonance peaks. For the ME structure with acrylonitrile-butadiene-styrene (ABS) trestles, the resonance peak was different for different places of the NdFeB permanent magnet. Besides, the maximum of the ME coefficient was 4.142 V/A at 32.2 kHz when the NdFeB permanent magnet was on top of the Terfenol-D layer. Compared with the ME coefficient with a DC magnetic field, the ME coefficient with NdFeB magnets still maintained high values in the frequency domain of 65~87 kHz in the ME structure with mica trestles. Through Fourier transform analysis of the transient signal, it is found that the phenomenon of multiple frequencies appeared at low field frequency but not at high field frequency. Moreover, the output ME voltages under different AC magnetic fields are shown. Changing the amplitude of AC magnetic field, the magnitude of the output voltage changed, but the resonant frequency did not change. Finally, a finite element analysis was performed to evaluate the resonant frequency and the magnetic flux distribution characteristics of the ME structure. The simulation results show that the magnetic field distribution on the surface of Terfenol-D is non-uniform due to the uneven distribution of the magnetic field around NdFeB. The resonant frequencies of ME structures can be changed by changing the location of the external permanent magnet. This study may provide a useful basis for the improvement of the ME coefficient and for the optimal design of ME devices.

Wave propagation in microtubules is investigated based on the nonlocal elastic theory. The complete analytical formulas of wave velocity are obtained, and the results demonstrate that the small scale effect can reduce the velocity, especially for large longitudinal wave-vector and large circumferential wave number. When the wave length is smaller than 80 nm, the small scale effects are more significant. The results match the conclusions of lattice vibration well. Besides, temperature is taken into account and the results show that the temperature effect on waves in microtubules is not monotonous but have a certain stableness in higher and lower temperature zone. The methods and results may also support the design and application of nano devices such as micro sound generator etc.

The complex structure of the superconducting strand and different mechanical and thermal properties of the component materials make its mechanical behavior difficult to be predicted well, and some experimental phenomena are hard to explain, for example, the “platform” in the stress–strain curve of the powder-in-tube (SMI-PIT) strand. Thus, developing better numerical models is very necessary. In this paper, taking the SMI-PIT strand and internal tin (LMI) strand as examples, their stress–strain characteristics under tensile load at different temperatures are simulated with finite-element method models. In these models, the complex internal structure, the initial thermal residual stress, and the damage of the filament and its evolution are taken into consideration. The “platform” in the stress–strain curve of the SMI-PIT strand is explained commendably, the relevant influence factors about this “platform” are discussed, and the reason why this “platform” does not occur in the curve of the LMI strand is also explained. From the discussion, we find that the distribution of the break points in the filaments will affect the slope of this “platform,” and the initial crack decides the start point of the platform. The calculated results agree well with the experimental data.

The transport performance of Nb 3 Sn cable-in-conduit conductors (CICCs) depends on the strain distribution along the superconducting filaments determined by the combination of electromagnetic and mechanical forces applied to the strands. The aim of this paper is to analyze the electromagnetic-mechanical coupling behavior of Nb 3 Sn strand by establishing a 3-D finite-element model. This model contains subdomains, which are air region, superconducting filaments, and metal matrix. The mechanical constitutive relations of superconducting filaments and metal matrix are described with elastic and elasto-plastic strain-stress experimental curve, respectively. For the voltage-current (V-I) characteristic, metal matrix elements follow the Ohmic law, and superconducting filaments are modeled with the n-power relation. Lorentz force in three directions (x, y, and z) caused by the external magnetic field and induced current are calculated. The current density and magnetic field distribution of strand are also computed, and the results show the filaments prevent a further field penetration from the outer into the interior matrix. The combination effect of the tensile force and Lorentz force on the strand is discussed. It can be found that Lorentz force combined with the tensile force makes the degradation obvious. The model provides a basis to analyze the electromagnetic-mechanical coupling behavior of the Nb 3 Sn strand and be able to predict the current flow patterns and magnetic field distribution.

A theoretical model is established for nonlinear magnetoelectric (ME) effect and harmonic distortion behavior in laminated composite, in which the complex nonlinear mechanical-thermo-magnetic characteristics of magnetostrictive phase are taken into consideration. Both the low-frequency and the resonant ME effects are derived by the elastic mechanics method. In this model, the output ME voltage is divided into three parts: a dc term, a linear ac term and a nonlinear ac term. Considering the temperature effect, this model is adopted to predict the dependences of ac voltages on bias magnetic field, frequency of ac magnetic field, the volume fraction of piezoelectric phase and interfacial parameter. Then, the competition relationship between linear and nonlinear ac voltages is discussed. To clearly describe the nonlinear characteristics of the proposed sample, a distortion factor θ is used for characterizing the harmonic distortion behaviors. The dependences of θ on the frequency of ac magnetic field and temperature under different ac magnetic fields are also studied. Finally, the predictions of harmonic distortion behaviors with changing bias magnetic field are obtained. The calculated linear ME coefficient shows a good agreement with the previous experimental data. It showed that: linear ac voltage and linear piezomagnetic coefficient present the same trend as the bias magnetic field increases, and nonlinear ac voltage shows the same trend as the absolute value of nonlinear piezomagnetic coefficient with increasing bias magnetic field; with temperature increasing, the output ME voltages decrease; operating temperature has a minimal effect on the required magnetic field corresponding to the optimal value of the output ME voltages, while it cannot alter the optimal value of piezoelectric phase's volume fraction; the nonlinear ac voltage presents more resonant frequencies than the linear one in the same range. Also, a definite multiple relationship is observed between the corresponding resonant frequencies of linear and nonlinear voltages; a larger θ leads to a more serious harmonic distortion, which is influenced by the frequency of ac magnetic field and temperature; bias magnetic field can be applied to adjust the harmonic distortion behaviors.

A nonlinear dynamic hysteretic theoretical model on magnetoelectric effect of tri-layered composites is built based on a nonlinear constitutive relation for magnetostrictive material and a linear piezoelectric model for piezoelectric material. And a finite element analysis is implemented to investigate quantitatively the influences of hysteresis and temperature on the ME effect of the layered composites. The model also can explain the “self-biased” response caused by the hysteretic characteristics of the ME composites. Then the distribution of the true displacement along the longitudinal direction is revealed by numerical calculation. The increment of temperature due to the magnetic hysteresis loss is investigated. The temperature, the AC magnetic field and the bias field on the induced electric field and the ME effect are studied, respectively. The results show that the bigger the magnetic frequency, the larger the energy loss of the ME composites. The initial temperature has little effect on the induced electric field at low magnetic field region, but significant effect on the induced electric field at high magnetic field region. The frequency multiplying behavior will disappear when the bias field is strong. In addition, the bias magnetic field also affects the shape of E 3 ∼ H AC curve, with the increase of the bias field, the shape of E 3 ∼ H AC curve changes from symmetry to asymmetry. The frequency mixing of the induced electric field is also discussed.

We develop a magneto-elastic (ME) coupling model for the interaction between the vortex lattice and crystal elasticity. The anisotropies in superconductivity and elasticity are simultaneously included in the GL theory frame. Under this consideration, the expression of the free energy unifies the different forms of the classical results. Concerning the ME effect on the magnetization, the theory can give a satisfying description for the field dependence of magnetization near the upper critical field. The contribution of the ME interaction to the magnetization is comparable to the vortex-lattice energy, in materials with relatively strong pressure dependence of the critical temperature. While the magnetization components along different vortex frame axes are strain dependent, the magnetization ratio is independent of the ME interaction. It is stressed that the GL description of the magnetization ratio is applicable only if the applied field moderately close to the upper critical field.

ITER magnetic device (Tokamak) requires a strong magnetic field produced by charged cable conductors and external sources to arrive at stable and reliable magnetic confinement performance. Before manufacturing and assembling conductors, preliminary analysis of self-field induction is helpful for reducing the cost of varying-parameter experiments. Spatial helix shape of numerous strand elements and multi-level twist of the finalized cable, known as CICC type, make it unpractical to direct use finite-element methods and other numerical procedures for self-field calculation. An algorithm FDBS (fast direct Biot–Savart integration) is proposed to surmount this difficulty, which improves the traditional method (DBS, direct implementing Biot–Savart law for all strand sources) in terms of computational effort. As such the complexity reduces to O(N) from the original O(N2) and speed enhancement is achieved in the parallel computation environment. FDBS calculates out a detailed self-field profile for the uncompressed ITER TF conductors carrying uniform current at each cabling level; the layered self-field distribution becomes more indistinct for higher level subcable.

Magnetoelectric (ME) effect in a Ni/PZT/Terfenol-D composite cantilever was tested under three different magnetic loading modes. The frequency-dependent ME effect and dual-peak phenomenon were observed in the experiment. The influence of orientations of magnetic fields on the dual-peak phenomenon of ME coupling was investigated. Magnetic field distribution inside the ME composite structure was simulated, which agrees well with experimental data. The experiment results indicate that ME coefficient versus bias magnetic field curve presents a novel dual-peak phenomenon near the resonant frequency, and the ME coefficient which depends upon the amplitude and orientation of magnetic field presents a nonlinear shift whether at the resonant frequency or not. In addition, the optimal angle corresponding to the largest ME coefficient for different bias fields were obtained. The proposed ME composites-based sensors can be used for detecting or harvesting magnetic signals of uncertain orientations and amplitudes in complex environments.

An unexpected degradation frequently occurs in superconducting cable (CICC) due to the mechanical response (deformation) when suffering from electromagnetic load and thermal load during operation. Because of the cable's hierarchical twisted configuration, it is difficult to quantitatively model the mechanical response. In addition, the local mechanical characteristics such as strain distribution could be hardly monitored via experimental method. To address this issue, we develop an analytical model based on the hierarchical approach of classical wire rope theory. This approach follows the algorithm advancing successively from n + 1 stage (e.g. 3 × 3 × 5 subcable) to n stage (e.g. 3 × 3 subcable). There are no complicated numerical procedures required in this model. Meanwhile, the numerical model is set up through ABAQUS to verify and enhance the theoretical model. Subsequently, we calculate two concerned mechanical responses: global displacement–load curve and local axial strain distribution. We find that in the global displacement–load curve, the elastic–plasticity is the main character, and the higher-level cable shows enhanced nonlinear characteristics. As for the local distribution, the friction among adjacent strands plays a significant role in this map. The magnitude of friction strongly influences the regularity of the distribution at different twisted stages. More detailed results are presented in this paper.

Recent researches highlight the additional anisotropic crystallographic axis within the superconducting plane of high temperature superconductors (HTS), demonstrating the superconducting anisotropy of HTS is better understood in the biaxial frame than the previous uniaxial coordinates within the superconducting layer. To quantitatively evaluate the anisotropy of flux pinning and critical current density in HTS, we extend the scaling rule for single-vortex collective pinning in uniaxial superconductors to account for flux-bundle collective pinning in biaxial superconductors. The scaling results show that in a system of random uncorrected point defects, the field dependence of the critical current density is described by a unified function with the scaled magnetic field of the isotropic superconductor. The obtained angular dependence of the critical current density depicts the main features of experimental observations, considering possible corrections due to the strong-pinning interaction.

Although numerous studies have shown that contact resistance depends significantly on roughness and fractal dimension, it remains elusive how they affect contact resistance between rough surfaces. The interface similarity index is first proposed to describe the similarity of the contact surfaces, which gives a good indication of the actual contact area between surfaces. We reveal that the surfaces’ similarity be an origin of contact resistance variation. The cyclic loading can increase the contact stiffness, and the contact stiffness increases with the increase of the interface similarity index. These findings explain the mechanism of surface roughness and fractal dimension on contact resistance, and also provide reference for the reliability design of the electrical connection.

This paper presents an analysis on electromagneto-thermo-mechanical behaviors of conductive plates, an analytical solution is given for a conductive circular plate in a time-dependent magnetic field by using a T-method of the eddy current which is widely used in the eddy current analysis of conductive and superconductive structures. The solution is expressed in an analytical series form and it is suitable for a circular plate under any arbitrary axisymmetric magnetic fields changing in time. Some interesting results including the eddy current, the increment of temperature, and the electromagneto-thermal stresses are investigated, respectively, in this paper. Some characteristics such as the distribution of temperatures, the in-plane electromagnetic stresses and the dynamic response of the conductive plate are first studied and displayed. This study not only reveals some characteristics on the eddy current, the temperature of the plate, the in-plane electromagnetic thermal stresses and the dynamic responses of the conductive plate which is in a time-dependent magnetic field, but presents a new possible way to simplify the analysis of the electromagnetic coupling problem for conductive structures.

In this study, a novel functionally graded cylindrical magnetoelectric (ME) composite based on d15 shear-mode response is analyzed theoretical by using the elastic mechanics model and equivalent circuit model. The composite is mounted around AC current-carrying power lines to scavenge AC magnetic field energy. For different sensing configurations, the generated magnetic fields are calculated, respectively. Then, based on the theoretical models, the dependences of the ME performances, i.e., the ME voltage and power, upon the type of the material gradation, the material constants, and geometrical parameters of the cylindrical ME composite are numerically evaluated. The results show that the ME coupling effect in the functionally graded cylindrical ME composite with special gradation is stronger than that in the homogeneous structure. The ME performance can be improved by geometrical parameters as well. The presented two models can be synthesized under the open-circuit condition, which provide a theoretical basis to understand and improve the ME property of the d15 shear-mode cylindrical ME composites operating at resonant frequency and off-resonance frequency.

In previous works, most of them employ a linear constitutive model to describe magnetocapacitance (MC) effect in magnetoelectric (ME) composites, which lead to deficiency in their theoretical results. In view of this, based on a nonlinear magnetostrictive constitutive relation and a linear piezoelectric constitutive relation, we establish a nonlinear model for MC effect in PZT-ring/Terfenol-D-strip ME composites. The numerical results in this paper coincide better with experimental data than that of a linear model, thus, it’s essential to utilize a nonlinear constitutive model for predicting MC effect in ME composites. Then the influences of external magnetic fields, pre-stresses, frequencies, and geometric sizes on the MC effect are discussed, respectively. The results show that the external magnetic field is responsible for the resonance frequency shift. And the resonance frequency is sensitive to the ratio of outer and inner radius of the PZT ring. Moreover, some other piezoelectric materials are employed in this model and the corresponding MC effects are calculated, and we find that different type of piezoelectric materials affect the MC effect obviously. The proposed model is more accurate for multifunction devices designing.

We build a 3D model to analyze the electromagnetic behaviors of Nb3Sn filamentary strand exposed to a time-varying current injection, under the consideration of n value and strain effect. Electromagnetic behaviors, performance degradation and AC loss are investigated. Results show that the filament bundles prevent a further field penetration from the outer shell into the interior matrix. Different current/field profiles occur in the strand and outside. Compared to the critical current, the average transport current keeps a high value with little change over a broader strain range, and has a larger magnitude by several orders of magnitude. Increasing the strain results in a suppression of the current transport capacity, and part of the current is expelled into the metal matrix causing larger AC loss. The larger twist pitch implies a longer current circuit and more magnetic flux enclosed, thus increasing the loss. More details are presented in the paper.

A nonlocal anisotropic elastic shell model of a microtubule (MT) has been established in this paper. The proposed model exactly expresses the persistence length, the growth rate for buckling and the buckling load which include the small scale effects in a closed form. The predicted results of our model indicate that the length-dependence of the persistence length is sensitive to the small scale effects when the length of the MT is short. The curves for the growth rate of a MT with the consideration of the small scale effects show that the larger the small scale parameter is, the larger the growth rate is. The buckling behavior of a MT with the consideration of the small scale effects and the filaments network surrounded the MT have been investigated, which presents the filaments network plays an important role in buckling behaviors of MTs.

Future accelerator magnets are pushed to their limits in terms of magnetic field, mechanical strength and from the quench protection point of view. This forces the magnet designers to re-think the quench modelling. One issue that has not so far been largely explored is the mechanical behaviour of the superconducting coils during a quench. This can cause limitations to the design of high field accelerator magnets. This paper focuses on mechanical behavior in the event of a quench of a Nb3Sn 16 T dipole magnet currently developed in the framework of the EuroCirCol project in view of the Future Circular Collider conceptual design study. The thermo-mechanical analysis is performed through finite element modeling. The analysis takes into account the Lorentz force and the thermal stress due to the non-uniform temperature distribution in the winding during a quench. acceptedVersion