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In the AC loss simulation, it is a huge challenge to model the twisted wire at the filament level, due to the complex structure as well as long-time computation consumption. In this paper, we use 3D finite-element method based on H-formulation to study the AC loss in a twisted superconducting wire. The wire is treated as a homogenous material with the anisotropic conductivity in the filament region. We quantitatively simulate the AC loss induced by the AC transport current and magnetic field profile, and the effect of the twist pitch on the AC loss. In the case of AC transport current, larger pitch length leads to higher loss, and the pitch length effect is contrary to the case of applied magnetic field. The influences of the magnetic field direction and non-uniform current distribution subjected to the strand bending are also investigated. It is observed that, the transverse magnetic field has a more significant influence on the AC loss than the longitudinal magnetic field. The non-uniform current distribution can result in a higher AC loss, compared to a corresponding uniform current distribution.

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.

A two dimensional (2D) mechanical-magneto-thermal model of direction-dependent magnetoelectric (ME) effect in Terfenol-D/PZT/Terfenol-D laminated composites is established. The expressions of ME coefficient at low and resonance frequencies are derived by the average field method, respectively. The prediction of theoretical model presents a good agreement with the experimental data. The combined effect of orientation-dependent stress and magnetic fields, as well as operating temperature on ME coefficient is discussed. It is shown that ME effect presents a significantly nonlinear change with the increasing pre-stress under different loading angles. There exists an optimal angle and value of pre-stress corresponding to the best ME effect, improving the angle of pre-stress can get more prominent ME coupling than in x axis state. Note that an optimal angle of magnetic field gradually increases with the rise of pre-stress, which can further lead to the enhancement of ME coefficient. Meanwhile, reducing the operating temperature can enhance ME coefficient. Furthermore, resonance frequency, affected by pre-stress, magnetic field and temperature via “ Δ E effect”, can enhance ME coefficient about 100 times than that at low frequency.

Considering the magneto-mechanical coupling of magnetostrictive material, the tunability of in-plane wave propagation in two-dimensional Terfenol-D/epoxy phononic crystal (PC) plate is investigated theoretically by the plane wave expansion method. Two Schemes, i.e. magnetic field is rotated in x–y plane and x–z plane, are studied, respectively. The effects of amplitude and direction of magnetic field, pre-stress and geometric parameters are discussed. For Scheme-I, band gap reaches the maximum at an optimal angle 45° of magnetic field. However, the optimal angle is 0° for Scheme-II, because band gap decreases monotonically until disappears with the increasing angle. For both cases, higher-order band gaps generate and become stronger as magnetic field amplitude increases, while increasing compressive pre-stress has the opposite effect. Meanwhile, filling fraction plays a key role in controlling band gaps. These results provide possibility for intelligent regulation and optimal design of PC plates.

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 study, a new kind of magnetoelectric (ME) structure is designed with Terfenol-D, PZT-5A and nonmagnetic and nonelectric trestle. The configuration of this ME structure presents “A-line” type, PZT-5A and Terfenol-D are respectively bonded with the trestles, which adopt the knuckle joint assembly. Differently from the conventional ME layered structure, in the new structure, the deformation of the PZT-5A of larger size is driven by a Terfenol-D layer of smaller size at an external magnetic field. Since the driven force is applied at the ends of piezoelectric layer through the trestles, the whole piezoelectric layer can be completely stretched or compressed, and the larger voltage should be induced. For the new ME structure with mica trestle, the maximum value of α E is twice higher than that for the conventional laminated ME structure. Furthermore, a wider range of response frequency is also observed in this structure. For the new ME structure with ABS trestle, the experimental results indicate that the maximum ME voltage coefficient is measured as high as 31.85 V/cm Oe at 405 Oe.

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 spontaneous magneto-elastic (ME) interaction dictates the coupling between vortex arrays and crystal lattice, triggered by the spontaneous vortex nucleation in mixed state. In Ginzburg–Landau theory, the pinning interaction is ascribed to the interaction energy of first-order defect strain field and spontaneous elastic field. The pinning force is therefore estimated as the force on a dislocation imposed by the spontaneous stress field. Subsequently, the first-order pinning is compared with the weak collective pinning quantitively. The magnetization contribution by the first-order pinning is a parabolic dependence with field H, while the magnetization of the collective pinning shows a severe suppression at high fields as H−3. The difference in magnetization is attributed to the energy characterization in pinning mechanisms. As for the critical current density, the combination of first-order and collective pinning generally reproduces the experimental data of Ba0.75K0.25Fe2As2 sample where the second magnetization peak (SMP) disappears. In this view, the elasticity effect in mixed state is sufficient to cause the vanishment of SMP, especially in samples with high pressure dependence of Tc.

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.

The aim of this article is to present a three-dimensional (3D) simulation based on Voronoi tessellation, used to assess the strain dependence of the superconducting critical properties of inhomogeneous polycrystalline Nb3Sn at the microstructural level. To support this objective, we first present a polycrystalline model with equiaxed grains used to analyze the relationship between the polycrystalline structure and the strain response. We analyze the Young's moduli of Nb3Sn at different temperatures with random and preferential polycrystalline orientations, and the relation between the Young's modulus of polycrystalline Nb3Sn and spontaneous tetragonal transformation is discussed. The results indicate that the elastic properties (Young's modulus, stress/strain field) of polycrystalline Nb3Sn are mainly associated with ambient temperature and phase transition and are affected by the grain orientation. Meanwhile, an estimation-based model for the superconducting critical properties of single-crystal Nb3Sn is proposed. This model is based on changes in the electron density of states and phonon frequency induced by strain. The results calculated by the estimation-based model are consistent with the experimental data and the values calculated according to first principles. The change in the strain-induced superconducting properties of polycrystalline Nb3Sn is analyzed by combining the numerically simulated strain field of the polycrystal with the estimation-based model of single-crystal Nb3Sn. Compared to ideal single-crystal Nb3Sn, the superconducting critical temperature of the polycrystalline Nb3Sn superconductor has a higher strain sensitivity, which is related to the non-uniformity of the strain field of the polycrystal.

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.

Phononic crystals are widely researched for new kinds of functional composites. However, studies on magneto-elastic PCs at nanoscale that show special superiorities are quite limited. Considering the nonlocal effect and nonlinear magneto-mechanical coupling, this work establishes a theoretical model for size-dependent flexural wave band structure of magneto-elastic PC nanobeams with magnetostrictive materials according to the Euler–Bernoulli beam model and nonlocal theory. The influence of nonlocal parameter, pre-stress and magnetic field on band structure of Titanium/Terfenol-D PC nanobeams is analyzed. The results show that the nonlocal effect has a remarkable weakening impact on the dispersion curve of high order band gap. In addition, band gap exhibits complex nonlinear coupling characteristics due to the consideration of pre-stress and magnetic field. Moreover, geometric parameter plays an important role in determining the size-dependent band structure. Consequently, the research may be helpful for flexible regulation of elastic wave propagation in PC nanobeam-based devices.

The bending behaviors of superconducting strand with typical multi-filament twist configuration are investigated based on a three-dimensional finite element method (FEM) model, named as the Multi-filament twist model, of the strand. In this 3D FEM model, the impacts of initial thermal residual stress, filament-breakage and its evaluation are taken into accounts. The mechanical responses of the strand under bending load are studied with the factors taken into consideration one by one. The distribution of the damage of the filaments and its evolution and the movement of the neutral axis caused by it are studied and displayed in detail. Besides, taking the advantages of the Multi-filament twist model, the normalized critical current of the strand under bending load is also calculated based on the invariant temperature and field strain functions. In addition, the non-negligible influences of the pitch length of the filaments on both the mechanical behaviors and the normalized critical current are discussed. The stress-strain characteristics of the strand under tensile load and the normalized critical current of it under axial and bending loads resulting from the Multi-filament twist model show good agreement with the experimental data.

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.

In this paper, a mechanical-thermo-magneto model for self-biased magnetoelectric effect in laminated composite with high-permeability materials is established. Considering the effects of demagnetization, pre-stress and temperature, the effective magnetic field and piezomagnetic coefficient of magnetostrictive layers are calculated. Then, the effects of temperature and pre-stress on ME effect are investigated. Finally, the combined effect of temperature and pre-stress on zero-bias ME voltage coefficient is discussed in detail to achieve a good ME conversion efficiency. The numerical results show that due to the occurrence of the additional magnetic field from high-permeability materials, available self-biased ME effect can be obtained in the proposed model. The operating temperature affects not only the peak value but also the initial value of ME voltage coefficient. Also, pre-stress can change the temperature effect on the zero-bias ME voltage coefficient obviously.

The superconducting strand, serving as the basic unit cell of the cable-in-conduit-conductors (CICCs), is a typical multi-filament twist composite which is always subjected to a cyclic loading under the operating condition. Meanwhile, the superconducting material Nb3Sn in the strand is sensitive to strain frequently relating to the performance degradation of the superconductivity. Therefore, a comprehensive study on the mechanical behavior of the strand helps understanding the superconducting performance of the strained Nb3Sn strands. To address this issue, taking the LMI (internal tin) strand as an example, a three-dimensional structural finite element model, named as the Multi-filament twist model, of the strand with the real configuration of the LMI strand is built to study the influences of the plasticity of the component materials, the twist of the filament bundle, the initial thermal residual stress and the breakage and its evolution of the filaments on the mechanical behaviors of the strand. The effective properties of superconducting filament bundle with random filament breakage and its evolution versus strain are obtained based on the damage theory of fiber-reinforced composite materials proposed by Curtin and Zhou. From the calculation results of this model, we find that the occurrence of the hysteresis loop in the cyclic loading curve is determined by the reverse yielding of the elastic–plastic materials in the strand. Both the initial thermal residual stress in the strand and the pitch length of the filaments have significant impacts on the axial and hysteretic behaviors of the strand. The damage of the filaments also affects the axial mechanical behavior of the strand remarkably at large axial strain. The critical current of the strand is calculated by the scaling law with the results of the Multi-filament twist model. The predicted results of the Multi-filament twist model show an acceptable agreement with the experiment.

Superconducting performance of a large-scale Nb3Sn cable-in-conduit conductor (CICC) is degraded by periodic bending of strands subjected to a distributed transverse electromagnetic force during operation. The current transport in a single strand depends mainly on the bending strain and transverse resistivity. In particular, in the case of high-level strain and/or crack occurring among the filaments in the strain-sensitive Nb3Sn strand, these two parameters are required for better understanding of the critical current Ic degradation of a single strand. We use finite element method to simulate transport properties of a single Nb3Sn strand under bending. The simulation allows treating a wider range of transverse resistivity of strand, compared with our previous analytical method (Cryogenic, 58, 2013). Also, the present simulation incorporates the change of the area of strand cross section due to filament fracture into the boundary of the current transport, rather than simply imposes the condition of vanishing current on the filament fracture region as in the previous analytical method. We show the current/field profiles in the strand for various bending loads and transverse resistivities, as well as the Ic degradation of several types of strands under bending.

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.

An elastic model to predict radial vibration of ultra-small nanoparticles is proposed and the main reason of frequency shifts (comparing with classical elastic model) in ultra-small nanoparticles is interpreted. Taking the curvature-dependent surface theory into account, the effects of surface on the radial vibrations of nanoparticles are investigated with our new model. Both the atomic and the present models are calculated and their results agree well. It argues that the surface effects are remarkable on the radial vibrations of ultra-small nanoparticles and surface elasticity plays the main role rather than surface stress which is the previous understanding. The curvature-dependence of surface effects cannot be ignored when the particle is small enough. For the low-order radial vibration, the surface effects are more noteworthy.

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.

At present, conventional low-temperature superconductors such as Nb3Sn strands have been extensively applied in high-energy and nuclear physics, as well as in magnetic resonance imaging systems. In this paper, a 3D finite element model considering sophisticated structure of superconducting filament bundles and metal matrix elements is built to deal with the electromagnetic behaviors of a Nb3Sn strand exposed to tension and bending loads. The mechanical constitutive relations of filament bundles and metal matrix are described with elastic and elasto-plastic axial stress–strain curve, respectively. The voltage–current characteristic of the metal matrix elements is determined with the Ohmic law, and that of the superconducting filaments follows the n power relation. The stress–strain state is simulated and then implemented in the electromagnetic model, through the scaling law of ITER Nb3Sn strand. We find that the plasticity of copper and the twist filaments cause the enhanced inhomogeneous strain profile in a strand composite, compared to the strain profile in a strand with untwisted filaments. We also discuss the current/field profile, critical current degradation, and AC loss in the strand composite under the tension and bending loads.

A novel linear-shaped thermoelectric generator (Liner-TEG), due to its unique structure in which the p- and n-type thermoelements can be optimized independently, usually exhibits better design flexibility than a traditional pi-shaped thermoelectric generator (pi-TEG). In this study, the influence of the length ratio of the thermoelements theta= L-p/(L-p + L-n) on the output power and conversion efficiency of Linear-TEGs is investigated for different total lengths and heights of the thermoelements. And the predictive models on the thermoelectric performance under two operating temperature conditions are built, individually. The results show that, the maximum power and maximum efficiency are obtained at different length ratios; none of these maximums appears at the length ratio theta = 0.5. This implies that in contrast to pi-TEGs, the Linear-TEG has a better thermoelectric performance. Meanwhile decreasing the total length and/or increasing the height can improve the power. Interestingly, under the large temperature difference, there is a nonlinear relationship between the power and the height, and the optimal length ratio corresponding to maximum efficiency is dependent to the total length and height of the thermoelements, which are different to that under the small temperature difference. Our work will provide an alternative way for the design of high performance thermoelectric generators. (C) 2014 Elsevier Ltd. All rights reserved.

The conversion efficiency is the most important indicator describing the thermoelectric performance of thermoelectric (TE) devices. Under large operating temperature difference, the efficiency can be enhanced by the fabrication of segmented thermoelements structure. For running safety, the thermomechanical behavior of TE devices must be considered. In this paper, a 3D finite element model is established to estimate the TE and mechanical performance of the segmented thermoelectric generator (STEG) under optimal operating conditions. The effects of the segment lengths on the TE conversion efficiency and the maximum stress level of TE materials are examined at a given operating temperature. And for different operating temperatures, the maximum conversion efficiency and maximum stress level of TE materials are also investigated, individually. By the mechanical strength evaluation and mechanical reliability analysis, the TE behaviors of STEG are verified. The results indicate that, for a given operating temperature, some segmented cases do not satisfy the strength requirements, and the theoretical maximum efficiency does not equal to the actual optimal one; for different operating temperatures, the STEG cannot always achieve the maximum design value of conversion efficiency. These findings will have some significant positive impact on the optimal design and practical application of the STEG.

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.

We study snap-through transition and morphology of multilayer graphene on an elastic substrate, which has power-law grading modulus. It is indicated that both the inhomogeneous thickness and graded parameter of substrate have effects on corrugation and snap-through transition of graphene. The increase of graded parameter of substrate results in less corrugation of graphene. The snap-through transition of graphene is more likely to happen for larger graded parameter or thickness of substrate. This work provides theoretical guidance to control graphene morphology by changing the substrate thickness and grade in certain case.

Based on a linear piezoelectric relation and a nonlinear magnetostrictive constitutive relation, A nonlinear magnetoelectric (ME) effect model for flexural layered ME composites is established in in-plane magnetic field. In the proposed model, the true coupling stress and the equivalent piezomagnetic coefficient are taken into account and obtained through an iterative approach. Some calculations on nonlinear ME coefficient are conducted and discussed. Our results show that for both the flexural bilayer and trilayer composites, the true coupling stress in the composites first increase and then approach to a constant value with the increase of applied magnetic fields, affecting the nonlinear ME effect significantly. With consideration of the true coupling stress, the ME effect is smaller than that without consideration of the true coupling stress. Moreover, the proposed theoretical model predicts that the ME coefficient of the trilayer composite (does not generate the bending deflection) is much larger than that of bilayer composite (generates the bending deflection), which is in well agreement with the previous works. The influences of the applied magnetic field on the true coupling stress and fraction ratio corresponding to the extreme ME coefficients of layered structures are also investigated.

A theoretical model taking into consideration the interface effects is established to predict the Seebeck coefficient and the electrical conductivity for a polycrystalline thermoelectric (TE) thin film. The interface scattering mechanisms (including the film-surface scattering and grain-boundary scattering) of the transport electrons in the film materials are revealed. The relations between the Seebeck coefficient, the electrical conductivity and the interface parameters (the film-surface reflection coefficient and the grain-boundary transmission coefficient) are then discussed with respect to the proposed model. The differences in the TE properties between the films and bulk materials caused by size restriction are investigated. The results indicate that the higher grain number leads to stronger grain-boundary scattering and more distinct size effects of the TE properties. In contrast to the surface effect, the grain-boundary effect plays a main role in the TE properties of TE films with polycrystalline structures.

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.

The present study investigated the intelligent control of both band gaps (BGs) and energy harvesting based on the point defect of magneto-elastic acoustic metamaterial and piezoelectric effect. The numerical results obtained by the finite element method indicate that band structures and frequency range of acoustic energy harvesting can be modulated significantly by an applied magnetic field, which leads to broadband BGs and promotes the electromechanical energy conversion efficiency. Consequently, the proposed structure can provide new avenues for designing of both tunable acoustic insulator and a broad-distributed energy harvester in engineering fields. © 2019 The Japan Society of Applied Physics.

The heat removal capability and the coolant pumping costs in the design of cable-in-conduit conductors are depend on the thermo-hydraulics of the liquid helium flow. Therefore, the accurate knowledge of the thermo-hydraulics of the flow is significant for the design of the cables, especially for permeability. In this paper, the fractal method is proposed to describe the cable cross-section and an approximate expression is derived. Then, a fractal permeability model for helium flow in CICCs is presented based on a porous medium analogy. The feasibility and validity of this model is verified by the comparison of the predicted values and the experimental values. The fractal model indicates that permeability of cables is determined by the cable geometric parameters, such as the effective porosity, the average cabling angle, the average diameter of strands and the pore area fractal dimension of the cable cross-section. This model does not contain any empirical constants or fitting constants and can be used to explain the mechanism and to predict the permeability of the helium flow in CICCs. Furthermore, the effects of cable geometric characteristics on the presented fractal permeability model are also analyzed and simulated. The results imply that permeability of cables decreases with increasing the cabling angle, increases with the effective porosity, the pore fractal dimension and the average diameter of the strands increase. These results are consistent with the physical situations.

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.

Intrinsic current flow and field distribution scheme under the imposed low current injection and the applied weak field is meaningful to interpret Ic degradation and AC loss in a strand that performs as a normal composite conductor. A 2D finite element (FE) transport model is built in COMSOL to identify the various transverse resistance components and reveal the interrelation among them. Then the transverse resistivity components are taken as the basic electrical components in a 3D composite strand model. The 3D model follows the realistic trajectories of twisted filaments in strand composite and experimental material properties. To address the potential/current map in the stationary transport, the FE model is thoroughly analyzed for the short-sample and long-sample strand, imposed by two in-plane steady current injections and a potential boundary condition at one strand end with the other end grounded, respectively. The results show that the short-sample longitudinal current is uniform with little resistivity loss, and flows from the positive source and converges to the negative one in the cross section with different paths and current proportions between filaments and matrix. However, for the long-sample, there is a serious reduction in electric potential along the strand axis and the currents mostly concentrate on filaments. The time-varying problem is also implemented by computing AC loss induced by a relatively far-away alternating line current. It is discussed where appropriate that the effect of the twist pitch and contact resistivity on the pattern and magnitude of the current flow and AC loss.

Nb3Sn strand critical current (Ic) degradation is a basic issue strongly related to ITER operating performance. The developed analytical scheme predicting Ic degradation takes into account transverse resistivity and irreversibility of strand composite. Once compared to the measurements on three types of strands in periodic bending tests, this analytical prediction almost eliminates the difference between the measurements and widely existing previous models. As transverse resistivity gets closer to the experimental value, the prediction approaches the measurement remarkably. Additionally the classical outstanding experiment for strand in a steel tube simulating the practical operating situation is interpreted with this improved scheme. It is concluded that the discrepancy between Ekin’s model result and the measurement is primarily due to the intrinsic transverse resistivity and irreversibility limit.

We study the morphology and snap-through transitions of multilayer graphene on a corrugated elastic substrate whose surface roughness is determined by surface amplitude and wavelength. Based on the couple stress theory, we develop a theoretical model to understand the size effect on the graphene morphology. It is indicated that the surface amplitude has no effect on the corrugation of graphene, whereas increased surface wavelength results in greater corrugation of the graphene on the substrate. At high surface roughness, a snap-through transition is more likely to happen. Moreover, our results show obvious size effect on the graphene morphology for high surface roughness and compliant substrates. This work offers theoretical insights to control graphene morphology by changing the substrate surface roughness.

Considering the nonlinear coupling behavior of magnetostrictive material, the modulation of Lamb wave bandgaps in magneto-elastic phononic plates composed of Terfenol-D pillars on a silicon matrix is investigated by the finite element method. By the introduction of holes, two schemes, i.e., the pillars only case for scheme-I and the trampoline (pillars and holes) case for scheme-II, are considered for exploring the effect of magnetostriction and trampoline on band structures. Numerical results show that the edges of bandgaps shift toward higher frequencies and the relative bandwidth enlarges as the magnetic field increases. The greater the compressive pre-stress applied, the greater the magnetic field at the open or closed points of the bandgap required. Compared to scheme-I, we find that the existence of holes for scheme-II can cause the closing of the higher branches’ bandgaps and the generation of a new bandgap, and larger relative bandwidth of the bandgap and wider range of the required magnetic field can be observed due to the trampoline effect. Meanwhile, the height of the pillar is a key parameter for generating or vanishing bandgaps. According to the displacement distribution of eigenmodes, it can be seen that the opening or closing of the bandgap is controlled by the coupling between Lamb modes of the plate and resonant modes of the pillars, which is induced by the combined effect of trampoline, magnetic field, and pre-stress as well as geometry parameters. These results give guidance for active controllability of Lamb wave propagation and intelligent regulation of phononic devices 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.

Recently TARSIS measurements (Test Arrangement for Strain Influence on Strands) have been conducted for Nb 3 Sn strand’s critical current I c under periodic bending strain, to stimulate the real situation in operating CICC. Based on the Ciazynski and Torre’s formulae (Supercond. Sci. Technol. 23, 2010), we propose an improved scheme, further revealing the intrinsic mechanism for TARSIS. Especially the obtained transverse transport map well characterizes the inter-filament transfer, which shows clearly two pathways of the electric field and the filament twist dependence of the current. Meanwhile, the improved scheme is extended to describe the generalized transport properties, and predict V – I characteristic within a wide resistive range. The V – I curves illustrate the shift from typical power law behavior to less precise power law behavior with loading increasing. These results are helpful for future strand experimental design.

The effect of electric charge on the mechanical properties of graphene under tensile loading is investigated by using molecular dynamics method. A modified atomistic moment method based on the classical electrostatics theory is proposed to obtain the distribution of extra charges induced by an external electric field and net electric charges stored in graphene. The electrostatic interactions between charged atoms are calculated using the coulomb law. The results show that the Young’s modulus and the critical fracture stress under uniaxial tension decrease with the increase of electric potential and net charges on graphene. The failure of graphene induced by electric charges is found to be controlled by charge level. The results indicate that the carbon-carbon bonds at the edge of graphene will break first.

Transport AC losses play a very important role in high temperature superconductors (HTSs), which usually carry AC transport current under applied magnetic field in typical application-like conditions. In this paper, we propose the analytical formula for transport AC losses in HTS wire by considering critical current density of both inhomogeneous and anisotropic field dependent. The angular dependence of critical current density is described by effective mass theory, and the HTS wire has inhomogeneous distribution cross-section of critical current density. We calculate the angular dependence of normalized AC losses under different DC applied magnetic fields. The numerical results of this formula agree well with the experiment data and are better than the results of Norris formula. This analytical formula can explain the deviation of experimental transport current losses from the Norris formula and apply to calculate transport AC losses in realistic practical condition.

In this study, we investigate the nonlinear coupling magneto-electric (ME) effect of a giant magnetostrictive/piezoelectric composite cylinder. The nonlinear constitutive relations of the ME material are taken into account, and the influences of the nonlinear material properties on the ME effect are investigated for the static and dynamic cases, respectively. The influences of different constraint conditions on the ME effect are discussed. In the dynamic case considering nonlinear material properties, the double frequency ME response (The response frequency is twice the applied magnetic frequency) is obtained and discussed, which can be used to explain the experiment phenomenon in which the input signal with frequency f is converted to the output signal with 2 f in ME laminated structures. Some calculations on nonlinear ME effect are conducted. The obtained results indicate that the nonlinear material properties affect not only the magnitude of the ME effect in the static case but also the ME response frequency in the dynamic case.

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.