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The second-generation high-temperature superconductor (HTS) tape is a promising material for the HTS application. However, the extremely large aspect ratio of the HTS coated tape leads to high power dissipation in the environment of a time-varying magnetic field. Reducing the width of HTS coated tape is a feasible way to decrease the alternating current (AC) loss of devices composed of HTS tapes. In this study, a numerical model of the HTS coil group composed of six sub-coils based on the T-A formulation is presented in which each HTS sub-coil is wound with original or narrow width Y-Ba-Cu-O (YBCO) tape. The 1/3 and 1/4 narrow width tapes are used to represent the tapes, which are divided into three and four equal parts, respectively. Then, we calculate the AC losses in 1/3 and 1/4 narrow width HTS coil groups in different cases. The estimated results of AC loss are compared with those of the HTS coil group wound by HTS tapes with original width. The numerical results show that AC transport losses of 1/3 and 1/4 narrow width HTS coil groups are smaller than that of the original HTS coil group for the applied high current. Furthermore, with the decrease in tape width, the reduction of AC loss becomes more significant. In contrast with the original width HTS coil group, the magnetization losses of the 1/3 and 1/4 narrow width HTS coil groups will decrease at the high magnetic field. In addition, the influences of harmonic components on AC loss are also considered. [ABSTRACT FROM AUTHOR]

A bulk superconductor in a high magnetic field is subjected to a large electromagnetic force, which can cause crack propagation and damage the bulk. In this paper, we study the fracture behavior of the GdBCO bulk superconductor under a large electromagnetic force based on the Extended Finite Element Method (XFEM). The critical state Kim model and H-formulations are used to obtain the electromagnetic force of a bulk superconductor in the magnetic field first. Second, the Stress Intensity Factor (SIF) of the bulk superconductor for various cracks under the electromagnetic force is presented. Numerical results show that the SIF depends not only on crack angle and length but also on the width of the bulk. For the inclined crack with a large crack angle, with the crack length increase, the SIFs increase first and decrease, while for a small crack angle, the SIFs decrease with the crack length increase. For the kinked crack, the SIFs decrease with the crack length increase. With the XFEM, the growth of the inclined and kinked cracks in the bulk superconductor during field cooling is presented. The crack propagation paths are dependent on the size of the bulk and different for two crack problems. In the process of crack propagation, the propagation path has a certain degree of deflection angle compared with the initial crack. [ABSTRACT FROM AUTHOR]

Numerical simulations of the electro-mechanical behavior in arrays of superconducting tapes are presented in this paper. The superconducting properties of tapes are influenced not only by the local magnetic field but also the mechanical strain. The mechanical strain will reduce the critical current density and lead to the degradation of superconductivity. Due to the nonlinear E − J behavior, it is difficult to analytically obtain the two-dimensional current and magnetic field distributions. We use the magnetic energy minimization method based on the field-dependent critical current density to determine the distributions of the current and magnetic field in arrays of rare-earth-barium-copper-oxide (REBCO) tapes. Next, the finite element method is employed to calculate the mechanical strain and stress distributions, and the anisotropic mechanical properties of the REBCO tapes are adopted. The numerical method is verified with the analytical solution for a one-dimensional single tape with transport current. The strain and stress distributions in superconducting tapes are calculated for different transport current/external magnetic field conditions. The relationship between the stress and the number of tapes in the arrays is discussed, and the effect of the distance between adjacent tapes on the stress is also investigated. The results may be beneficial to the design of superconductor magnets. [ABSTRACT FROM AUTHOR]

The degradation of critical current due to mechanical deformation in a high field has a profound impact on the performance of high-temperature superconducting (HTS) structures. The multi-layer conductor on round core (CORC) cable is a widely-applied HTS structure in engineering. Due to the complexity of the multi-layer CORC cable, the contact between the tapes should be considered when simulating the mechanical behavior in high field. In this paper, 3D electromagnetic and mechanical models were developed to investigate the mechanical behavior of the multi-layer CORC cable. Under the same electromagnetic force, the comparisons of mechanical models of a 5-layer CORC cable with different contact methods are presented. Subsequently, the effects of the loading path of the external magnetic field and transport current, the bending geometry of the CORC cable, the winding direction of the HTS tape in the CORC cable, and the shielding current on the mechanical behavior are discussed, respectively. The numerical results are useful for the design and operation of CORC cable in high field. [ABSTRACT FROM AUTHOR]

For the accurate prediction of the effective thermal conductivities of the twisted multi-filamentary superconducting strand, a two-step homogenization method is adopted. Based on the distribution of filaments, the superconducting strand can be decomposed into a set of concentric cylinder layers. Each layer is a two-phase composite composed of the twisted filaments and copper matrix. In the first step of homogenization, the representative volume element (RVE) based finite element (FE) homogenization method with the periodic boundary condition (PBC) is adopted to evaluate the effective thermal conductivities of each layer. In the second step of homogenization, the generalized self-consistent method is used to obtain the effective thermal conductivities of all the concentric cylinder layers. The accuracy of the developed model is validated by comparing with the local and full-field FE simulation. Finally, the effects of the twist pitch on the effective thermal conductivities of twisted multi-filamentary superconducting strand are studied. [ABSTRACT FROM AUTHOR]

• The incremental Mori-Tanaka method is adopted to study the thermo-elasto-plastic behaviors of twisted multi-filamentary superconducting strands and structures. • The twisting of the superconducting filament is considered by rotational transformation along the helical filament. • The accuracy and efficiency of the developed model are assessed by comparing with direct numerical simulations. • The mechanical behaviors of the superconducing strands and structures are studied using the developed model. An efficient estimation of the thermo-elasto-plastic behaviors of twisted multi-filamentary superconducting strands and structures is crucial for the superconducting conductor design and application. In this paper, an incremental Mori-Tanaka method is adopted to study the thermo-elasto-plastic behaviors of twisted multi-filamentary superconducting strands and structures. The mechanical behavior of copper matrix is described by nonlinear kinematic hardening plasticity and numerically realized using a midpoint algorithm. The effect of the twisted filament is considered by rotational transformation along the helical filament. The incremental Mori-Tanaka method is integrated into finite element simulation using the UMAT subroutine in ABAQUS. The applicability of the developed model is validated by comparing with direct numerical simulations. Then, the comparison with experimental results shows that the incremental MT method can characterize the experimental results effectively. The macroscopic mechanical behaviors of twisted multi-filamentary superconducting strands with different twist pitches are studied, and the thermal loading is considered. Finally, the idealized superconducting structure analysis is conducted to illustrate the application of the developed incremental MT method on a larger scale. [ABSTRACT FROM AUTHOR]

Bulk superconductor is subjected to a combination of huge electromagnetic force and temperature rise owing to the rapid movement of magnetic flux during pulsed field magnetization (PFM). Meanwhile, the heat generated will decrease the shielding effect and limit the strength of trapped field in turn. In view of its intrinsic brittle property and existing defects in fabrication, the bulk is prone to fracture under the complicated electromagnetic and thermal loadings. In this paper, the fracture behavior and damage evolution of the bulk superconductor with two or more cracks during PFM are investigated. Based on the electromagnetic field and temperature obtained by solving governing equation of H -formulation and heat transfer equation, the mechanical behavior of bulk is simulated with ordinary state-based Peridynamic model. The dynamic stress intensity factors considering thermal stress at crack tips are studied for different external magnetic fields and crack angles. Then, the influences of thermal contact resistance and local heat source are discussed. Finally, crack propagation in the bulk samples without reinforcement is modelled during PFM. • Multiple cracks problem in bulk superconductor during pulsed field magnetization. • The dynamic SIFs of multi-cracks are obtained using OSPD. • The effects of TCR and local heat source on energy release rate are discussed. • The propagations of randomly distributed cracks are modelled. [ABSTRACT FROM AUTHOR]

The hard-magnetic soft materials which can sustain high residual magnetic flux density gradually attract the attention of researchers because of potential applications in soft robotics and biomedical fields. In this work, we focus on the dynamic response of hard-magnetic soft materials. The dynamic motion equations are derived by the Euler-Lagrange equation. The effects of the aspect radio on the nonlinear vibration of the hard-magnetic soft cuboid under the force and applied magnetic fields in different directions are investigated. The amplitude-frequency curves demonstrate that the aspect ratio also has an influence on the frequency and amplitude of the primary resonance. Moreover, to eliminate undesired vibration responses, the PID controller is applied to the vibration of the hard-magnetic soft materials, and the desired results can be obtained. [ABSTRACT FROM AUTHOR]

The Fast Fourier Transform (FFT) method was used to simulate the magnetization problems of the thin film in a perpendicular magnetic field. There are few works on the calculations of the superconducting film with transport current using the FFT-based method. To take into account the effect of the transport current, we modify the previous method and then use it to calculate the electromagnetic behaviors of the thin film. This modified method is implemented by transforming the boundary conditions of the transport current. The numerical results are compared with the integral solution for accuracy and the T–A formulation in finite elements for efficiency. The results show that the FFT-based method is an efficient method for the calculations of the superconducting film carrying transport current. Next, we simplify the 2D film problems to the infinitely long strip situation and use the modified method to calculate the strip stack problems. The results indicate that the modified FFT-based method is also valid for the computation of the strip stack problems and efficient as the number of strips is not very large. [ABSTRACT FROM AUTHOR]

The High Luminosity Large Hadron Collider (HL-LHC) is one of the large-scale projects currently being developed at the European Organization for Nuclear Research (CERN). Many Nb 3 Sn superconducting magnets are employed in this project, which exhibit complicated multiscale characteristics. The mechanical behaviors of magnets, which are directly related to the safety and stability of the overall structure, are affected by the electromagnetic–mechanical-thermal loading in actual service conditions. However, detailed modeling of magnets requires significant computing resources. A reduced-order method named self-consistent clustering analysis (SCA) has been proposed recently to reduce the cost. We have combined the SCA and finite element method (FEM) as an efficient multiscale framework, which is utilized to analyze the mechanical behaviors of accelerator magnets. Firstly, the computation results by presented framework are compared with direct numerical simulation (DNS) and existed experimental data to validate the accuracy and efficiency. Then, the FEM-SCA2 framework is utilized to study the mechanical behaviors of MQXFS accelerator magnet model under assembly, cool-down and excitation steps. The influences of material parameters, friction coefficient and stiffness degradation are also discussed. This paper provides an efficient multiscale analysis framework for investigating mechanical behavior in Nb 3 Sn accelerator magnet, which could be employed to study other magnets. [ABSTRACT FROM AUTHOR]

Due to the excellent electromagnetic properties of superconductor materials, superconducting generators have higher efficiency, lower weight and volume than traditional rotating machines. However, it is difficult to simulate the electromagnetic behavior in the superconducting generator due to the nonlinear E–J relationship. A numerical model based on the T–A formulation and moving mesh method is adopted to simulate the superconducting rotating machine, and the electromagnetic and mechanical behaviors of the superconducting rotating machine are investigated. The fully superconducting generator investigated in this article is radial type, which consists of field windings and armature windings made from YBa2Cu3O7−Δ (YBCO) superconducting race-track coils. The anisotropic field-dependent critical current density and the E–J power law relationship are considered in our model. The “virtual tape” model is introduced to calculate the induced current in the T–A formulation. The numerical results are obtained by the finite element method. The electromagnetic results calculated by our model are compared with results from the H–A formulation. The ac losses and stress distributions in superconducting coils are presented based on the T–A formulation. The results show that the body force and stress are periodic, and the stress will concentrate on the boundary of the coil. The magnetic field in the rotor is larger than that in the stator, and the field windings suffer greater body force and stress than the armature windings. This model has acceptable relative error with the H–A model for the time saved following T–A approach and relevance to mechanical calculations. Thus, this model can aid the design of superconducting rotating machines. [ABSTRACT FROM AUTHOR]

In this paper, the critical state Bean model is employed to estimate the effect of the electromagnetic force on the fracture behavior of the superconductor slab. The superconductor slab with an inclined crack is subjected to an applied field. Based on the finite element method, the stress intensity factors are computed for two activation processes, zero field cooling and field cooling. Numerical results obtained show that the crack length and the inclined angle have significant effects on the fracture behavior. Generally, maximum of mode-I stress intensity factor is larger than that of mode-II stress intensity factor. The stress intensity factors analyzed in the paper are useful to learn fracture behavior and mechanical failure of superconductors. [ABSTRACT FROM AUTHOR]

• A coupled electromagnetic-mechanical model is built to calculate the coupling behaviors of superconducting coils. • Mechanical deformation impacts the motion of magnetic flux and changes the critical current of superconductors. • The roles of contact conditions in the superconducting coils are derived theoretically. • A mechanical homogenization model is proposed to simplify the model containing hundreds of contact pairs. Rare-earth based barium copper oxide (REBCO) superconducting coated conductors are promising candidates for the design of high field magnets. In a high magnetic field, these conductors have to withstand huge Lorentz force, which would threaten the safety of superconducting devices. Recently, researchers have found that the electromagnetic-mechanical coupling has a significant impact on the overall response of the magnet system. It has been demonstrated that mechanical deformation can lead to the movement of magnetic flux in superconductors and changes in the critical current of superconductors. To take into account the electromagnetic-mechanical coupling effects, REBCO coated conductors are modeled as deformable conductors based on continuum mechanics of electromagnetic solids. Then, a fully coupled electromagnetic-mechanical model is developed in this paper, which is verified with the experimental results. Furthermore, during the electromagnetic-mechanical coupling simulation, contact separation occurs in REBCO pancake coils. To characterize the global mechanical performance of the REBCO pancake coils (containing hundreds of contact conditions), the concept of flexural rigidity in elastic shell theory is employed. Then, a mechanical homogeneous model is proposed to simplify the model containing hundreds of contact pairs and enable the effective simulation of large-scale HTS systems. This framework can provide theoretical support to the mechanical research of high field magnets. [ABSTRACT FROM AUTHOR]

This paper studies the transport critical current density in a superconducting cylinder with a hole and a superconducting elliptic cylinder. Based on the Maxwell's equation, the critical current densities are obtained with numerical method for different cross sections. In order to determine the main features of different cross sections, the average critical current density and magnetic field are considered. It is shown that the average critical current density is affected by the geometry and size of the cross section. The average critical current density is a monotonic function of the radius in the superconducting cylinder with a hole. However, the average critical current density in the superconducting elliptic cylinder decreases with major axis first and then increases. [ABSTRACT FROM AUTHOR]

The strain effect on critical magnetic field in isotropic high-κ superconductors is studied theoretically in this paper. Based on the phenomenological theory, we obtain the critical magnetic field in the presence of the applied strain. The dependence of upper critical magnetic field on the coupling parameters is discussed. The theoretical analysis is in broad agreement with experimental results as the coupling parameters are the linear functions of the strain. Furthermore, according to the assumption, the plot of strain effect on lower critical field is observed as symmetric curve for compressive and tensile strains. The plots also predict that the strain effect on lower critical field is greater in higher-κ superconductors. [ABSTRACT FROM AUTHOR]

The multi-filamentary Bi 2 Sr 2 CaCu 2 O 8-x (Bi2212) round wire is the candidate for high field magnets, which is macroscopically isotropic and has large critical current in high field. AC losses generated in coils by ac transport current and magnetic field will lead to the rise of local temperature and consumption of liquid helium. However, the simulations of AC losses in coils are limited by the complicated geometry. This paper presents a homogenization model for computing the current density distributions, field distributions and AC losses in coils wound by multifilament Bi2212/Ag round wire. Based on two-dimensional axisymmetric H-formulation (H is the magnetic filed), the field dependent critical current density and the nonlinear relation between the electric filed E and the current density J are used to describe the macroscopic behavior of the superconductor. To validate the homogenization model, the AC loss is compared with the result of origin model which has the actual filament configuration of round wire. The homogenization model is powerful to estimate the AC losses of cables and coils made by Bi2212/Ag round wire. [ABSTRACT FROM AUTHOR]

In this work, the influence of the shear deformation on the depairing current density in superconducting film is analyzed theoretically. The modified effective free energy is proposed by relating the dependence of the order parameter on the shear deformation. Based on the elastic theory, it is assumed that the coupling energy is the sum of volume change energy and shear strain energy. We obtain the complex deformation dependence of the depairing current density. The results reveal that the shear deformation plays an important role in degrading the current density. © 2012 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The interface crack problem in the superconducting film-substrate structure under the magnetic field is investigated. A solution of the two-dimensional magnetoelastic problem is found. It is assumed that the plane stress state of deformation prevails in the structure. We take into consideration both cases of interface crack in the film-substrate structure and the superconductor slab. The fracture behaviors are considered for the non-superconducting substrate and superconducting substrate. Based on the simple geometrical and material assumptions, we express the explicit analytical description of the stress intensity factor and energy release rate. An increase of the stress intensity factor and energy release rate with the applied field has been observed. During the field reduction, the variations of the fracture behavior exhibit a complex characteristic. In addition, the effect of the deformation of the substrate is significant. This work may provide a tool for the analysis of the mechanical instability in the film-substrate structure. [ABSTRACT FROM AUTHOR]

The changes of the superconducting depairing current density with applied strain in superconducting films are studied theoretically in this paper. The thin film is assumed to be isotropic. Using phenomenological theory, we obtain the depairing critical current density in the presence of applied strain. The dependence of deparing current density on coupling parameters is discussed. A qualitative agreement between our theoretical predictions with reported experimental results is observed as the coupling parameters are linear function of the applied strain. The results indicate that the coupling parameters have a significant influence on the critical current density in the superconducting film. [ABSTRACT FROM AUTHOR]

• The electro-mechanical behaviors of coated conductors under different bending modes are numerically investigated through structural modeling. • The obtained strain distributions of the superconducting layer during bending are found to be related to the applied bending force. • The electro-mechanical behaviors of Q-IS strands under bending are analyzed based on the bending strain distributions obtained from structural modeling. The electro-mechanical properties of Rare-Earth Barium Copper Oxide (REBCO) coated conductors (CCs) are crucial for practical structures such as power cables, magnet coils and so on. Many tests including tension and bending tests were conducted to estimate the critical current of REBCO CCs under different loadings. However, standard test method for the electro-mechanical properties of REBCO CCs has not been established, especially for bending tests. Therefore, finite element simulations of bending tests of REBCO CCs are still needed to further analyze the electro-mechanical behavior under loading. Structural responses of REBCO CCs and quasi-isotropic (Q-IS) strands under bending are analyzed using continuum shell element in this study. The numerical results indicate that bending strains obtained from finite element simulations match well with the analytical calculations in pure bending state. Furthermore, the influences of former shapes are also discussed to evaluate the bending tolerance of REBCO CCs in different cases. In addition, the mechanical properties and critical current degradation of Q-IS strands under bending are analyzed. [ABSTRACT FROM AUTHOR]

The termination resistance can lead to the nonuniform distributions of current in the superconducting cable, which has an obvious effect on the quench characteristics. In order to study the quench in the infinitely long stacked-tape YBCO cable, a simplified two-dimensional (2D) model is established. By considering the termination resistances, the coupled heat conduction equation and the Maxwell's equations are solved to calculate the evolution of current and temperature with time, where E-J constitutive law and Ohm's law are used for the superconducting layer and other layers in the tape. Then, a 2D solid mechanical model is built to analyse the strain and stress during the quench. When the pulsed heat source is applied on the cable, it can be found that the termination resistance will affect the sequence of the quench of tapes in the cable. Meanwhile, the sequence and time of the quench are influenced by transport current and the locations of heat source. The distribution of the Von Mises stress is similar to the temperature, and the termination resistances have little effect on the mechanical behaviors. The strain rate has an inflection point when the temperature is more than the critical temperature. [ABSTRACT FROM AUTHOR]

Performance improvement of high-temperature superconducting (HTS) pancake coil is of paramount importance for its application in electrical facilities. In this paper, the utilization of ferromagnetic disks including weak magnetic material and strong magnetic material is investigated through numerical simulations for the aim of reducing the AC loss. Both the nonmagnetic and magnetic substrates are considered for the rare-earth-barium-copper-oxide coated conductor tapes wounded into the pancake coil. In order to analyze the influences of ferromagnetic disks on the maximum allowable currents and AC losses of nonmagnetic substrate-based coil and magnetic substrate-based coil, a self-consistent model based on the A-formulation is adopted to calculate the critical current and a 2D axisymmetric model built on the H-formulations is established to calculate the AC loss. According to the simulation results, it is found that ferromagnetic disks especially the strong magnetic disk are slightly detrimental to the critical currents of the pancake coils. Nevertheless, the presence of large background field weakens the effects of ferromagnetic disks. The simulation results also indicate that strong magnetic disks achieve about 50% reduction of the AC loss in the nonmagnetic substrate-based coil, and the AC loss of the magnetic substrate-based coil can be increased or reduced with strong magnetic disks depending on the applied current amplitude. The utilization of strong magnetic disks leads to the enhancement of the AC loss in the magnetic substrate-based coil at lower current and to the reduction of it at larger current. [ABSTRACT FROM AUTHOR]

We study the effect of different sizes and shapes of pinning centers on the vortex motion in superconducting strip in the presence of external current and magnetic field using the time-dependent Ginzburg–Landau theory. The size of pinning centers obviously affects the threshold current corresponding to the appearance of phase-slip line. The larger size results in a considerable decrease of the threshold current and a larger output voltage. For the same size, the different shapes of pinning centers lead to different behaviors of vortices. The dynamic behavior of vortices is dependent on the minimum distance d m between pinning center and the sample surface and the maximum length l m of the pinning center paralleling with the sample edge. However, the obvious changes are observed in the dynamic of vortex motion in superconductor with different pinning centers. [ABSTRACT FROM AUTHOR]

Highlights • The electromagnetic force is analyzed in superconductors during magnetization. • Crack paths under electromagnetic loading are predicted using peridynamics. • Quantitative elastic and fracture analyses of 2D structures are presented. • Voids and inclusions affect the crack propagation paths. Abstract Bulk high-temperature superconductors exhibit priority magnetic properties compared to the conventional permanent magnets. Single-grain bulk GdBaCuO superconductors have significant application potential due to higher critical current density J c and trapped fields. However, bulk superconductors are subject to larger Lorentz forces under high magnetic fields and their performance is limited by damage to the materials. In this paper, a finite element model based on the H -formulation is used to solve for the electromagnetic force in bulk GdBCO containing defects or inclusions under application of a pulsed field. Strong local electromagnetic force enhancement is observed at the crack tip. A bond-based peridynamic (PD) approach is proposed for analysis of the dynamic mechanical behavior and brittle damage of the sample. Crack initiation and propagation paths can be predicted using PD theory. PD is thus shown to be a suitable method for dynamic fracture problem analysis. As a further demonstration of the proposed model’s capabilities, the bulk fracture process is simulated. The effect of voids, cross cracks and multiple inclusions are presented. Results show that mechanical stability can be enhanced by the presence of silver particles. [ABSTRACT FROM AUTHOR]

Numerical calculations of mechanical behavior in multi-filamentary Ag-alloy sheathed Bi-2212 superconducting round wires and cables are presented in this paper. Bi-2212 composite wires possess excellent current carrying capabilities even in magnetic field. The strain may lead to the degradation of critical current density. And the filament fracture caused by strain is a key issue to the application of superconductor. Due to the complex nonlinear electromagnetic characteristics of superconductor, we use the variational formulation based on the field-dependent critical state model to calculate the distributions of current and magnetic field in Bi-2212 composite superconducting wires and cables. The finite element method (FEM) is employed in the calculation of mechanical behavior. We have developed a numerical method by combining the variational formulation and FEM to calculate the two-dimensional electro-mechanical problem. The strain and stress distribution in infinity long Bi-2212 single wire, two wires, 6-around-1 cable and Rutherford cable carrying transport current in external magnetic field are calculated. The possible damage position in wires and cables is discussed. [ABSTRACT FROM AUTHOR]

• The effect of the helical chirality on the local contact behavior is analyzed. • The 1D and 2D contact models are introduced to solve line and point contact forces. • The fretting wear factor of structures is calculated based on the Archard's equation. • The optimal designs of multilevel chiral helical structures are obtained by NSGA-Ⅱ. The local contact characteristics of multilevel chiral helical structures are critical, which determines the fretting wear and further affects the service life. In this paper, a theoretical model including global mechanical behaviors, local contact, and fretting wear is established. The ratio of the axial total moment to force is utilized to describe the load bearing capacity. Two kinds of models are developed for contact forces: 1D-explicit and 2D-iteration model, which are verified by the finite element method (FEM). The 1D model provides the explicit expressions of contact forces, meanwhile, the 2D model possesses the high accuracy under the short pitch. Different kinds of contact forces and the fretting wear are solved by the multilevel contact transmission law and the Archard's equation, respectively. Subsequently, the Pareto sets of multilevel chiral helical structures are obtained based on the theoretical model and the Non-dominated Sorting Genetic Algorithm-Ⅱ (NSGA-Ⅱ). Optimal designs with a strong load bearing capacity and a high fretting wear resistance are exhibited, which is useful to guide the design of multilevel chiral helical structures. [ABSTRACT FROM AUTHOR]

As a type of soft composite material, the hard-magnetic soft materials (HMSM) can retain high residual magnetization due to the high-coercivity of hard-magnetic particles. Meanwhile, the inherent viscoelasticity of the soft polymer matrix usually causes the rate dependent behavior and affects the stability of HMSM. The effects of viscoelasticity on the finite deformation and instability of HMSM are studied in this paper. A numerical model is developed for magneto-mechanical coupled problems of the viscoelastic HMSM. With this model, the instabilities of two typical HMSM structures (i.e. beam and spherical shell) with viscoelastic effects are investigated, including the buckling and snap-through instability. The results show that the viscoelastic effects delay the onset of instability and suppress the snap-back phenomenon during the unloading process. In addition, three different buckling behaviors (i.e. fully relaxed immediate buckling, elastic immediate buckling and the delayed buckling) at different loading rate ranges are observed in both beam and spherical shell. This work provides an effective numerical model to analyze the finite deformation and instabilities of viscoelastic HMSM and may guide the design of HMSM devices. • A numerical model is developed for the viscoelastic hard-magnetic soft materials. • The effects of the viscoelasticity on the instabilities of hard-magnetic soft materials are investigated. • Three different buckling behaviors at various loading rate ranges due to the viscoelasticity are captured. • The viscoelastic parameters and external magnetic field can adjust the delayed buckling behavior. [ABSTRACT FROM AUTHOR]

The second-generation high-temperature superconducting (HTS) coated conductor has been recognized as one of the most promising materialsfor high field magnets due to its superior electromagnetic and mechanical performances. HTS racetrack coils wound with the coated conductors are an extensively used configuration in engineering applications, such as HTS machines and high-speed maglevs. In this paper, in order to analyze the electromagnetic and mechanical behaviors of HTS racetrack coils, a 3D coupled electromagnetic-mechanical model is used to consider the effect of coil deformation and the strain dependence of critical current. The effectiveness of the coupled model is validated by comparing the numerical results with experimental data in the literature. A numerical simulation of a 3D HTS racetrack coil subjected to an external electromagnetic field is carried out using coupled and uncoupled models. The results indicate that the structure deformation can reduce the penetration depth of the screening current, and the hoop stress and strain are mainly concentrated on the circular part of the racetrack coil. Afterwards, the influences of various parameters on the electromagnetic and mechanical responses of the HTS racetrack coil are also investigated. [ABSTRACT FROM AUTHOR]

Since BiSrCa1CuO(Bi2212) wires are subject to mechanical loadings, degradation of critical current will occur. The effect of compressive loadings on the critical current of Bi2212 wire is studied by considering micro-buckling of filament. A Bi2212 wire is regarded as a unidirectional filament-reinforced composite in the theoretical analysis. By considering the influence of inclusion, the micro-buckling wavelength can be derived by using a two-dimensional model. Based on the experimental results, the critical current is fitted as a function of buckling wavelength. It is found that the decrease of the critical current is directly proportional to the reciprocal of square of the buckling wavelength. Change of micro-buckling wavelength with material parameters is discussed. A critical strain in the wire with a filament bridge is analyzed using the finite element method. [ABSTRACT FROM AUTHOR]

AC loss has become a key problem for practical applications of high-temperature superconductors. It is well known that mechanical deformation will affect the critical current and ac loss as the superconductor is subjected to the magnetic field or transport current. In this paper, the ac losses in Bi2Cr2Ca2Cu 3O10 (Bi2223)/Ag tapes under bending deformation are investigated. Bi2223 tape consists of Ag matrix and Bi2223 filaments, and the ac losses are generated by transport current and external field. By considering the plastic deformation of Ag matrix and residual strain, the simplified mechanical fracture model is established. Then, the finite element method analysis is used to investigate the relation of critical current and ac loss with bending deformations, and the losses are presented for different transport current and external magnetic field conditions. The influences of filament fracture on the ac loss are discussed for transport current and external magnetic field cases, respectively. [ABSTRACT FROM PUBLISHER]

Due to the low material cost, high critical transition temperature and high-current-carrying capacity, MgB round wire with twisted filaments has great potential for applications in engineering. Therefore, it is important to estimate their critical current for optimizing and realizing high-powered wire and cable. A 3-D model is presented to calculate the critical current of wire and cable with twisted filaments. The critical current is estimated based on the Biot-Savart law and self-consistent model. A comparison between 2-D and 3-D models is performed for the wire. We consider the effect of twist pitch on the critical current. Moreover, the critical current of 6-around-1 cable with different twist pitches is analyzed and discussed using the 3-D model. It can be found that twist pitch of filaments plays an important role on the critical current. The model and method may also be useful for other superconducting wires and cables. [ABSTRACT FROM AUTHOR]

• A modified theoretical model for the multilevel helical structures based on thin rod theory is proposed, where the global mechanical behaviors and the local contact effect are considered simultaneously. • The multilevel contact transmission law at different structural levels is proposed to reveal the relationship between the line and point contact forces. • The theoretical predictions including global mechanical and local contact responses are validated by finite element (FE) simulations. • The theoretical model has higher precision than the Costello model for high-level helical structures. Multilevel helical structures are widely applied in engineering and biological areas with complicated local contact of interwire and global mechanical behaviors. Based on the thin rod theory, we propose a theoretical model which can simultaneously calculate the global mechanical properties and the local contact behaviors of the multilevel helical structure. By considering the contact deformation and the periodic kinematic parameters (the curvatures and twist) of the high order helix, the quasi-static solution of the multilevel helical structure is derived under axial tension, and two types of contact forces including line and point are analyzed. The multilevel contact transmission law is proposed to reveal the relationship between the contact forces with different types and levels, and the tendency of two contact forces with pitch can be obtained. Compared with the Costello model, the deviation of global mechanical responses and finite element (FE) simulations is reduced for the high-level helical structure. The local contact forces from FE simulations are in agreement with the predictions of the present model. The effect of the structural parameters on the global mechanical responses as well as the local contact forces are analyzed according to the present model. Finally, based on an engineering practical cable, the global mechanical responses and local contact behaviors of the simplified cable structure are predicted under axial tension. This study contributes to the understanding of the transmission mode and mechanism of contact forces in the multilevel helical structure. [Display omitted] [ABSTRACT FROM AUTHOR]

Cables composed of rare-earth barium copper oxide (REBCO) tapes have been extensively used in various superconducting devices. In recent years, conductor on round core (CORC) cable has drawn the attention of researchers with its outstanding current-carrying capacity and mechanical properties. The REBCO tapes are wound spirally on the surface of CORC cable. Under extreme loadings, the REBCO tapes with layered composite structures are vulnerable, which can lead to degradation of critical current and even quenching of superconducting devices. In this paper, we simulate the deformation of CORC cable under external loads, and analyze the damage inside the tape with the cohesive zone model (CZM). Firstly, the fabrication and cabling of CORC are simulated, and the stresses and strains generated in the tape are extracted as the initial condition of the next step. Then, the tension and bending loads are applied to CORC cable, and the damage distribution inside the tape is presented. In addition, the effects of some parameters on the damage are discussed during the bending simulations. [ABSTRACT FROM AUTHOR]

The performance of Nb 3 Sn cable-in-conduit-conductor (CICC) shows a significant degradation with increasing electromagnetic load in the International Thermonuclear Experimental Reactor (ITER). As the strand is under the compression caused by adjacent strands, the strand damage may occur for high contact force. In this paper, we present a 3D helix model based on the TEMLOP and FEMCAM to simulate the contact force among the strands under transverse load. The maximum linear strain and indentation depth induced by contact stress are calculated with two-dimensional contact model of cylinder. The numerical results are compared with the experimental values. Finally, the indentation depth is discussed for different layers and cross angles based on two models. With the increasing of layer number, the degradation of performance will occur. The short bending wavelength leads to small indentation depth. [ABSTRACT FROM AUTHOR]

A theoretical model for calculating the stress and strain states of cabling structures with different loadings has been developed in this paper. We solve the problem for the first- and second-stage cable with tensile or bending strain. The contact and friction forces between the strands are presented by two-dimensional contact model. Several theoretical models have been proposed to verify the results when the triplet subjected to the tensile strain, including contact force, contact stresses, and mechanical loss. It is found that loadings will affect the friction force and the mechanical loss of the triplet. The results show that the contact force and mechanical loss are dependent on the twist pitch. A shorter twist pitch can lead to higher contact force, while the trend of mechanical loss with twist pitch is complicated. The mechanical loss may be reduced by adjusting the twist pitch reasonably. The present model provides a simple analysis method to investigate the mechanical behaviors in multistage-structures under different loads. [ABSTRACT FROM AUTHOR]

BiSrCaCuO (Bi-2212) round wires have outstanding electromagnetic behaviors in a high magnetic field. However, the filaments' fracture or gas bubble is difficult to avoid during the fabrication and application of Bi-2212 round wire, which would affect the critical current density seriously. In this paper, the engineering current density is studied based on Kim model for 7-bundle and 18-bundle wires with filament fracture by considering the effect of bridges between filaments. The distributions of critical current density of filaments are also investigated for different external fields. Finally, we present the relation between the number of cracked filaments and the applied strain. [ABSTRACT FROM AUTHOR]

BiCrCaCuO (Bi2223) composite tapes consisting of Bi2223 filaments, metal Ag and Ag alloy are usually exposed to a high magnetic field. The mechanical behaviour of composites is determined by the distribution and content of Bi2223 filaments in a magnetic field. Several Bi2223 composite tapes have different volume fractions of Bi2223 filaments, and the volume fraction is of fundamental importance in the determination of mechanical behaviour. In this paper, we present mechanical response to understand the effect of volume fraction of Bi2223 filaments. The critical current density is determined with consideration of the self field effect firstly. Then, the results of effective elastic moduli and mechanical stresses are presented based on the micromechanics approach. The mechanical response depends not only on the material properties but also on the Lorentz force. It is concluded from the computational results that the reduction of volume fraction of filaments can increase the mechanical stability, while the critical current density is decreased. Thus, it is necessary to consider both the mechanical limitation and requirement of the critical current of tape. [ABSTRACT FROM AUTHOR]

The Nb 3 Sn strands which have high critical field are used in cable-in-conduit conductors (CICCs). The superconducting strands are twisted multistage and experience complex thermal and electromagnetic loadings. Due to their brittleness, the cracking of the Nb 3 Sn filaments will occur under mechanical loading. In this paper, based on the linear elastic fracture theory, we study the effects of tension loading on the fracture behavior of central crack firstly. The strain energy release rates for different twist pitches and cabling stages are presented. As the triplet is subjected to the uniaxial strain, the cracking probability will increase with the twist pitch. The crack number increases with the applied strain, and wider filament or bronze can lead to smaller crack number under the same applied strain. In addition, multistage cabling has better mechanical stability. Next, the two collinear crack problem is considered. The variations of microcrack number show that the wider bronze can provide more resistance for the propagating of the large cracks. We can conclude that the bronze plays an important role in improving the stability and strength. [ABSTRACT FROM AUTHOR]

• Use the magnetic field and displacement in bulk superconductor to detect crack with Genetic Algorithm. • The magnetic field detection process is divided into two stages to enhance the detection capabilities. • The displacement detection is more effective than the magnetic field detection. In this paper, we use the magnetic field and displacement distributions to detect crack in bulk superconductors. The (Re)BCO bulk superconductors are ceramic oxides which have low mechanical strength. During the field cooling magnetization, the large Lorentz force will be generated in bulk superconductor, which will cause stress concentration near the cracks. When the local stress exceeds the fracture toughness, cracks will propagate and even cause damage of the bulk. In order to ensure reliability of bulk superconductor, it is necessary to determine location and size of crack. For bulk superconductor with a crack, the crack can also affect the magnetic field distribution. Firstly, we combine the Genetic Algorithm (GA) and magnetic field to detect crack in bulk superconductor. The values of position and shape information of crack in bulk superconductor can be obtained with objective function. After that, we obtain the electromagnetic force based on the magnetic field distribution. The Extend Finite Element Method (XFEM) with electromagnetic force is used to calculate the displacement of the bulk superconductor with a crack. The displacement and GA are also used to detect crack in bulk superconductor. Finally, we present a comparison between the magnetic field detection and the displacement detection. For horizontal crack, the displacement detection is more effective than the magnetic field detection. [ABSTRACT FROM AUTHOR]

As essential components, various types of solder joint structures including single-lap and bridge joints have been developed for the real applications and repair of the superconducting devices. Evaluations of the mechanical properties of these joints are usually performed using the tension (lap-shear) and bending tests. Degradation of critical current and an increase in joint resistance have been observed in these tests. Cracks in the superconducting layer and delamination between the coated conductors may lead to above degraded performance. In order to analyze the above electromechanical behavior of the single-lap and bridge joints, the responses of the single-lap and bridge joints under tension and bending tests are investigated through three-dimensional simulations. It is demonstrated that the numerical models can capture the stress concentration in the superconducting layer at the overlap edge of the joint under tensile tests. Furthermore, the bending radius is found to have a strong impact on the damage level of solder layer, and the damage pattern of the solder layer is related to the joint configurations. [ABSTRACT FROM AUTHOR]

The thermal residual stresses and strains are crucial in the industrial manufacturing process of the metal alloys and other composites. In representative volume element (RVE) of these complex composite structures, how to accurately and efficiently simulate the responses considering thermal residual stresses and strains is also vital, which could be served as a foundation to multiscale analysis. Recently an effective reduced-order method named self-consistent clustering analysis (SCA) has been proposed to solve microscopic responses in RVE. This paper modifies the original SCA method for thermoelastic and thermal elastoplastic problems, and the microscopic responses of the RVE are compared with the results of analytical and Fast Fourier Transform (FFT) methods to validate its accuracy and feasibility. Then, this study demonstrates the influences of different clustering strategies in offline stage, develops the clustering number optimization and discusses the two-scale analysis using the modified SCA method with/without thermal residual stresses and strains in microscale. In two-scale analysis, the macroscopic and microscopic responses are studied to explore the effects of thermal residual stresses and strains. The two-scale analysis framework with modified SCA method proposed in this work is proved to be efficient in simulating composites considering thermal residual strains and stresses. • Modification of the SCA with thermoelasticity and thermal elastoplasticity. • Different clustering strategies in offline stage are discussed. • Clustering optimization for SCA in two-scale analysis is used to reduce the cost. • Thermal residual stresses and strains are explored within two-scale analysis. [ABSTRACT FROM AUTHOR]

Abstract: The coupling effect between the mechanical behavior and the superconductivity is significant in deformable superconductors. In this article, electromechanical characterizations for the deformable superconductors in magnetic field are presented. We assume that the critical current density is independent of the magnetic field and strain effect on the critical current density is symmetric. The coupled partial differential equations are derived for the bulk superconductor. We quantitatively illustrate the effects of coupling parameters on the magnetostriction and magnetization. [Copyright &y& Elsevier]

Abstract: In order to interpret the two different kinds of experimental results of the effect of applied electric fields on the critical load at present, a new fracture criterion, the mechanical crack tip opening displacement (MCOD), is proposed in this paper. The fracture criterion predicts that the effect of applied electric fields on the critical load is different in two cases. The two theoretical results are all in according with the two kinds of experimental observations. It is interesting that the existing contrary experiments can be fully interpreted by the MCOD fracture criterion based on the results in this paper. [Copyright &y& Elsevier]

Abstract: The strip necking model for strain-hardening materials is studied in this paper, in which the stress distributed over the strip necking zone is assumed to be ultimate stress. The bi-linear stress–strain relation which can model certain features of plastic flow is adopted in this model. The stress and strain fields are calculated based on this model in this paper. The size of the strip necking region is determined by balancing the stress intensity factor due to remote loading with that due to assumed closing forces equal to the ultimate tensile strength of the material distributed over the strip necking zone. It is interesting that the strip necking region size and the crack tip opening displacement depend not only on the remote load, but also the material hardening parameters, which is different from the results of strip yield model. The results agree with experiments well, and the model has wider application. [Copyright &y& Elsevier]

In this paper, we investigate fracture behavior for the superconducting strip with a central crack by means of the finite-element method. The crack is assumed to be small enough such that the perturbations of the crack on the shielding current and the magnetic field are negligible. The Bean model where jc is field independent is adopted. We consider two cases, i.e., superconducting film with and without substrate. The stress intensity factors in the thin strip for the decreasing field are obtained. Compared with the case without substrate, the effect of the substrate on the stress intensity factor depends on the applied field Ba. [ABSTRACT FROM AUTHOR]

Accurate and efficient multiscale simulation of multifilament composite remains challenges due to expensive computation cost of solving the nonlinear representative volume element (RVE) responses in microscale. An effective reduced-order method called self-consistent clustering analysis (SCA) has been proposed recently to solve the dilemma. This paper extends the application of traditional multilevel finite element (FE2) to cylinder structure with domain division, where the inner domain is computed by finite element method (FEM) with SCA instead of direct FE2 method and outer domain is calculated by conventional FEM. The presented framework is named as concurrent modified FEM-SCA. To validate the accuracy and efficiency of presented method, the computation results of SCA, Fast Fourier Transform (FFT) and FEM are compared in microscale at first. Then, under the presented framework, the cylinder structures with diverse RVEs in uniaxial loading are studied, and the results are compared with full-scale direct numerical simulation (DNS) by FEM. Besides, the effects of different element positions, inclusion variations and loading phases on the RVE responses are also studied. [ABSTRACT FROM AUTHOR]

• The impacts of residual stress and viscoelasticity on the bifurcation and post-bifurcation behaviors of dielectric elastomer tube actuator with finite thickness are investigated. • The effects of voltage, axial force, and residual stress on the bifurcation and coexistence phase transition conditions are studied. • The competitive relationship between the localized bugling and electric breakdown is revealed. • The loading/unloading paths with the viscoelastic effect are explored. This paper investigates the impacts of residual stress and viscoelasticity on the bifurcation and post-bifurcation behaviors of dielectric elastomer tube actuator (DETA) with finite thickness. A theoretical model with residual stress is developed to analyze the electromechanical (EM) behavior of a DETA under a combined effect of voltage, internal pressure, and axial force loadings. A mathematical derivation of the bifurcation condition for the DETA under EM coupling loadings is presented, and a coexistence phase transition condition for steady bugle propagation is established. The effects of voltage, axial force, and residual stress on the bifurcation and coexistence phase transition conditions are studied. To validate the theoretical predictions, finite element (FE) simulations are performed on a closed-ended DETA subjected to the EM loadings. The results reveal a competitive relationship between the localized bugling and electric breakdown (EB). The large residual stress can inhibit the localized bugling and enhance the stability of the tube. Additionally, we explore the bifurcation behavior of the viscoelastic DETA, revealing that the viscoelastic effect significantly influences the critical pressure of bifurcation and the loading/unloading paths. It is observed that snap-back instability can occur during the unloading process under high loading rates or voltages. This work provides valuable insights into the finite deformation and bifurcation behaviors of the DETA under complex EM coupling loadings. [Display omitted] [ABSTRACT FROM AUTHOR]

• Delamination is analyzed using a coupled thermal–mechanical cohesive zone model. • Cohesive strength distribution has a remarkable impact on the delamination. • Influences of thermal-conductivity degradation caused by delamination are studied. Epoxy-impregnated pancake coil is observed to delaminate locally when its temperature is cooled from room temperature to 77 K. The delaminations cause the degradation of the critical current of the coil. Besides, the delamination may degrade the thermal conductivity and affect the thermal conductive path. Thus, in this study, the delamination behavior of epoxy-impregnated pancake coil during the cooling process is analyzed through a coupled thermal–mechanical cohesive zone model. The measured transverse tensile strength of coated conductors has shown considerable scatter and Weibull distribution has been adopted to fit the transverse tensile strength. The simulations are able to capture the main characterizations of the observed delaminations with the cohesive strength of the cohesive element following a Weibull distribution. After the cooling process, a heat spot is applied to the degraded positions to analyze the temperature field and the thermal conductive path in the damaged coil. Compared to the original undamaged coil, the delaminations indeed degrade the thermal conductivity and increase the thermal resistance. What's more, the effects of the variation of the thickness of the epoxy and different interfacial cohesive strength distributions of the coated conductor are considered. The results show that reduction of the thickness of the epoxy can lower the radial stress and release the damage, and the random distribution of the cohesive strength inside the coated conductor dominantly determines the delamination pattern of the coil. [ABSTRACT FROM AUTHOR]