A space–time fully decoupled formulation for solving wave problems with various nonlinearities is proposed based on sampling approximation for a function defined on a bounded interval by combining techniques of boundary extension and Coiflet-type wavelet expansion. By using a wavelet Galerkin approach for spatial discretization, nonlinear wave equations are first transformed into a system of ordinary differential equations, in which all matrixes are completely independent of time and never need to be updated in the time integration. Then, the classical fourth-order explicit Runge–Kutta method is employed to solve the resulting semi-discretization system. Several widely considered test problems are solved, and results demonstrate that the proposed wavelet algorithm has a much better accuracy and a faster convergence rate than many existing numerical methods. Finally, interactions of breather with strong attractive impurity in the sine-Gordon model are investigated by using the proposed wavelet method. Results show that a low-frequency breather with intermediate initial velocity can either pass the impurity, be trapped, be reflected, or break into a kink–antikink pair, depending sensitively on its initial phase. When the frequency of breather is the same as that of the impurity mode, it can always escape from the potential trap due to the severe resonance. These observations support that the proposed wavelet method is capable of capturing complex nonlinear phenomena, even those extremely sensitive to parameters.

The aim of this article is to analyze the strain distributions of filament bundles in the superconducting strands subjected to external mechanical loads and thermal strain. A multistage micromechanical model is adopted to characterize the mechanical behavior of the superconducting strand with twisted filaments. First, we employ the equivalent model to simplify the filament bundles. Then, the continuous filament bundles are divided into discrete elements, and an incremental mean-field micromechanics theme based on the Mori-Tanaka method is used to obtain the equivalent properties of the strand and the local strains in the Nb3Sn filament bundles. The results for two different structures are compared. The variation trends of normal strains along x, y and z directions are different. The effects of temperature on the equivalent properties of strands are discussed.

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.

•Both the interior flaw and the edge flaw are investigated.•Strong local enhancement of the current density in the vicinity of the flaw tip.•The influences of the size and position of the flaw on local current density.•The influence of the flaw on the AC loss of the sample is slight.This paper presents a finite element model based on the H-formulation to solve the electromagnetic behavior and AC loss in rectangular bulk superconductor with an elliptical flaw in AC external field condition. Both the interior flaw and the edge flaw are considered. A modified E–J power law which is valid for an arbitrary current density range is adopted in order to predict the strong local enhancement of the current density in the vicinity of the flaw tip. The results for the usual E–J power law are calculated for comparison as well. The simulation results show that the existence of the flaw significantly blocks the flow of the induced current and forces the current to redistribute around it. Meanwhile, the strong local enhancement of the current density is observed in the vicinity of the flaw tip. Furthermore, the influences of the size and position of the flaw on the local enhancement of the current density in the vicinity of the flaw tip are investigated. In addition, it is found that the influence of the flaw on the AC loss of the sample is slight for both cases of the interior flaw and the edge flaw.

In this study, we introduce a modified wavelet Galerkin method proposed recently by us to analyze the large deflection bending problems of thin rectangular plates, which are governed by the well-known von Kármán equations, consisting of two coupled fourth-order two-dimensional nonlinear partial differential equations. This adopted wavelet method is established based on a modified wavelet approximation scheme to interval-bounded L2-functions, in which each series-expansion coefficient can be explicitly expressed by a single-point sampling of the functions, and corresponding boundary values and derivatives can be embedded in the modified scaling function bases. By incorporating this approximation scheme into the conventional Galerkin method, the resulting algorithm can make the solution of the von Kármán equations become very effective and accurate, as demonstrated by the case studies that the wavelet solutions on the deflection–load relations have better accuracy and less consumed computing time than that of other numerical methods including the finite element method and the meshless method.

High-temperature superconductors in superconductor apparatuses are subjected to mechanical strains under operating conditions. These strains cause the degradation of the critical current densities and influence AC losses in the superconductors. Based on the dynamic process of thermomagnetic interaction, we report the results of numerical analysis of AC losses in an infinite high-temperature superconducting slab subjected to a uniform in-plane strain in an alternating external magnetic field parallel to the sample surface. The numerical analysis shows the details of electromagnetic phenomena in the slab and the dependences of AC loss on various external parameters including the uniform strain in the slab and the amplitude and frequency of the external magnetic field. In this paper, we find that whether the magnetic field fully penetrates the superconductor is the key factor that influences the features of AC loss. When the magnetic field cannot fully penetrate the superconductor, the loss rises with increasing strain or decreasing frequency. When the magnetic field can fully penetrate the superconductor, the feature is just opposite. We also analyze the effects of periodic strain on AC loss. It is interesting to find that when the periodic strain frequency equals the external magnetic field frequency, the AC loss reaches the maximum, regardless if the magnetic field fully penetrates the superconductor or not.

A numerical study on the influence of particle aspect ratio on the mechanical and structural properties of 2D sandpiles formed by means of a fixed height pointlike source is presented. The numerical results find that a clear dip in the vertical pressure is observed at the bottom and the extent of the dip increases with the increase of the particle aspect ratio. The particles tend to orient along the horizontal direction, which makes the orientation of contacts show a vertical tendency. The tendency becomes more obvious as the particle aspect ratio increases. There is the same contact orientation at which the Coulomb angle is equal to zero for all particle aspect ratios. The stronger force chains within the sandpiles orient preferentially in a direction with steeper slope for larger particle aspect ratio, and form more steady arches to support more weight of the sandpile.2D numerical simulation results indicate that the extent of the pressure dip increases with an increase of the particle aspect ratio. The stronger force chains orient preferentially in a direction with steeper slope for larger particle aspect ratios, and more steady arches are formed to support more weight of the sandpile.Highlights► Clumps are used to simulate the 2D sandpiles by the discrete element method. ► A clear pressure dip is observed at the bottom of the sandpiles. ► Increasing the particle aspect ratio will increase the extent of the pressure dip. ► The Coulomb angle is equal to zero when contact orientation is 67°for all cases. ► Strong arches are formed to support some weight of sandpile center.

•A novel generalized semi-analytical explicit capillary force model is established.•Fourier series expansion is introduced to fit for the plates with arbitrary shape.•Incredible ability to predict the standoff height when considering chip gravity.•Complex phase diagram is obtained to characterize varieties of system instability.Capillary forces induced by liquid meniscus are pivotal to many important technologies, including AFM measurement, powder technology, nano-objects manipulation and capillary driven self-assembly, etc. These forces (lateral, vertical and torque) are the object of substantial theoretical and numerical modeling, especially due to its significant influence on alignment reliability of fluidic self-assembly. To further understand the capillary interaction and misalignment mechanism, we propose a generalized semi-analytical capillary force model, extending the previous single-factor models to a unified one. With an ingenious meniscus deformation mode, surface energy and the associated capillary forces and torque are given simultaneously. The well accordance between model (when degenerated into previous single-factor modes) and Surface Evolver (SE) results indicates that the complex meniscus deformation process can simply be captured by translation and rotation of the “plate series” for small perturbations. Then the intercrossing effect on misalignment is systematically evaluated, from which we obtain a complex phase diagram (also confirmed by SE simulation) to characterize system local instability. It shows that angular misalignment is always associated with the lateral one, which is also observed in the existing experiment. Moreover, the presented model is suitable for other plates (binding sites) with arbitrary shapes.

We investigate the distribution of contact forces in a static granular system and in annular shear granular flow, using the discrete element method, and considering the influences of both packing fraction and friction coefficient. We find the existence of a critical packing fraction. If the packing fraction is lower than this critical value, all contact forces in granular system vanish. For shear granular flow, the critical packing fraction is significantly smaller than that for static granular system. The distribution of the contact forces also exhibits different forms, especially at lower packing fraction. We also investigate the spatial configuration of contact network using the angular distribution of contact forces. In static granular systems, the contact force network is approximately isotropic, while in shear granular flow, it exhibits a distinct anisotropy along the shear direction.

This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai’s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.

Highlights•The magnetic-elastic-thermal coupled constitutive model with eddy current effects is employed.•A nonlinear dynamic model with multi-fields coupling effects is established.•The results predicted by the model are coincident with the experimental data in quantity.•The effects of the dynamic stress and temperature on the effective magnetic field and ensuing magnetization are incorporated.•The dynamic components of the actuator such as spring loads and damping factors are considered.This paper addresses the modeling of complex hysteresis behavior for giant magnetostrictive actuator system under magnetically unbiased conditions. The hysteresis behavior is modeled by establishing a novel nonlinear dynamic model with multi-fields coupling effects, in which both the eddy current effects and the change of stress are considered. The former is included in the nonlinear transient constitutive model with magnetic-elastic-thermal coupling effect, which is employed as the basic constitutive equations of Terfenol-D. The latter is characterized through the structural dynamic behavior of actuator system itself, which is modeled by theorem of momentum. The quantitative agreements between numerical simulation results and existing experimental data indicate that nonlinear dynamic model can accurately describe the complex hysteresis behavior of the giant magnetostrictive actuator system not only under quasi-static operating conditions but also under dynamic operating conditions. The numerical simulation results also indicate that both the eddy current effects and structural dynamic behavior are the origin of frequency-dependent hysteresis behavior for giant magnetostrictive actuator system, and demonstrate the significance and necessity of simultaneously considering the eddy current effects and the change of stress in the system-level. Thus, the nonlinear dynamic model established in this paper is a system-lever coupled theoretical model, which can be directly used in the active vibration control and any other engineering application of the giant magnetostrictive actuators.

This paper focuses on eliminating the unphysical negative susceptibility which appears when magnetic field is at unsaturated excitation level and reduces from extremity of the hysteresis loop in one-dimension coupled hysteresis model. The domain flexing function c (H) is used to replace the domain flexing constant c in one-dimension coupled hysteresis model. The feasibility and rationality of proposed modification are convinced by comparing the magnetization and magnetostriction curves with experimental data and another typical modification results. The effects of pre-stress and temperature on magnetic-elastic-thermal coupling property and hysteresis behavior are investigated.

In the paper, the nonlinear magnetoelastic properties of composition Tb0.27Dy0.73Fe1.95 < 110 > oriented polycrystalline alloys are investigated under coupled loads of high magnetic field and compressive stress. The magnetization and magnetostriction are measured simultaneously under applied magnetic field from −800 to 800 kA/m and compressive stress from 0 to 25 MPa at room temperature. The strain coefficient and relative permeability are obtained by differential calculation from the experimental curves. The results show that the values of saturation magnetization (Ms) under different compressive stresses remain invariably constant in the region of the high magnetic field. The saturation magnetostriction (λs) increases with increasing compressive stress and reaches 1680 × 10−6 under 25 MPa. According to the increase of the compressive stress, the hysteretic loop area of magnetization and magnetostriction increases, while the maximum relative permeability and strain coefficient decrease. Additionally, the influence of the bias magnetic field on the mechanical property is taken into account. The stress-strain relationship is nonlinear and sensitive to the applied external magnetic fields along the axis of rod. The results obtained are a useful complement to the existing experiments for theoretical approaches and engineering applications.

•A hardening function is introduced to describe the degree of average hardening.•A new strip hardening model is proposed to investigate the hardening effect on CTOD.•The CTOD vs. the applied stress and overall strain is obtained analytically.•The CTOD depends on not only the applied stress, but also the hardening parameters.•The results of strip hardening model agree with the experimental results quite well.For a linear strain hardening material, we investigate the strain hardening effect on the crack tip opening displacement (CTOD) and obtain some interesting results. The nonlinear constitutive equation is simplified into a valid form, and a hardening function is introduced to solve this problem analytically. A new strip hardening model is proposed, and the strain hardening effect is limited in a sufficiently large zone which contains the crack. The hardening function is used to describe the degree of average strain hardening in this hardening zone for a given applied stress. Based on the strip hardening model, an analytical relationship between CTOD and remote applied stress is derived. It is interesting that both strip hardening zone size and CTOD depend on not only the applied stress, but also the hardening parameters. The theoretical results can agree with the experiments quite well by selecting an appropriate hardening function. Furthermore, the relationship between CTOD and overall strain is also obtained analytically in this paper. Compared with the experimental results, the strip hardening model is also valid to interpret the experimental results of the relationship between CTOD and overall strain. Therefore, we hope that the strip hardening model can be used to analyze more fracture behaviors for strain hardening materials.

A wavelet method for solving strongly nonlinear boundary value problems is described, which has been demonstrated early to have a convergence rate of order 4, almost independent of the nonlinear intensity of the equations. By using such a method, we study the bending problem of a circular plate with arbitrary large deflection. As the deflection increases, the bending behavior usually exhibits a so-called plate-to-membrane transition. Capturing such a transition has ever frustrated researchers for decades. However, without introducing any additional treatment, we show in this study that the proposed wavelet solutions can naturally cover the plate-membrane transition region as the plate deflection increases. In addition, the high accuracy and efficiency of the wavelet method in solving strongly nonlinear problems is numerically confirmed, and applicable scopes for the linear, the membrane and the von Karman plate theories are identified with respect to the large deformation bending of circular plates.

In this paper, a nonlinear and coupled constitutive model for giant magnetostrictive materials (GMM) is employed to predict the active vibration suppression process of cantilever laminated composite plate with GMM layers. The nonlinear and coupled constitutive model has great advantages in demonstrating the inherent and complicated nonlinearities of GMM in response to applied magnetic field under variable bias conditions (pre-stress and bias magnetic field). The Hamilton principle is used to derive the nonlinear and coupled governing differential equation for a cantilever laminated composite plate with GMM layers. The derived equation is handled by the finite element method (FEM) in space domain, and solved with Newmark method and an iteration process in time domain. The numerical simulation results indicate that the proposed active control system by embedding GMM layers in cantilever laminated composite plate can efficiently suppress vibrations under variable bias conditions. The effects of embedded placement of GMM layers and control gain on vibration suppression are discussed respectively in detail.

In this paper, the effect of magnetic nanoparticles on the mechanical properties of a type-II superconductor is investigated both theoretically and numerically. Magnetic part of the pinning force associated with the interaction between a finite-size spheroidal magnetic inclusion and an Abrikosov vortex is calculated in the London approximation. It is found that the size and shape of magnetic nanoparticles result in different enhancements of vortex pinning in large-κ type-II superconductors. Meanwhile, the screening current induced by a magnetic spheroid suffer the action of Lorentz force, which will lead to prestress in the superconductor, so further numerical calculations are needed to explore the interaction between the spheroidal magnetic particle and superconductor. The distribution of displacement, stress and strain in the superconductor are finally obtained. It is shown that different sizes and shapes of nanoparticles also can change the distributions of these quantities.

•The fracture behaviors of superconducting films for the Kim model are studied.•The profile of stress intensity factor is generally the same as magnetostriction.•The crack problem of two collinear cracks is also researched for the Kim model.The fracture behaviors under electromagnetic force with field-dependent critical current density in thin superconducting film are investigated. Applying finite element method, the energy release rates and stress intensity factors of one central crack versus applied field and crack length are obtained for the Bean model and Kim model. It is interesting that the profile of the stress intensity factor is generally the same as the magnetostrictive behavior during one full cycle applied field. Furthermore, the crack problem of two collinear cracks with respect to crack length and distance is also researched for the Kim model. The results show that the energy release rates and stress intensity factors of the two collinear cracks at left tip and right tip are remarkably different for relatively small crack distance and long crack length. This work can offer good estimations and provide a basis for interpretation of cracking and mechanical failure of HTS thin films in numerous real situations.

•A strong magnetic coupling appears if the gap between the superconducting rings is small.•The saturation magnetization of superconducting rings is related to the radial gap but independent of the vertical gap.•The array of rings in a non-uniform field experiences a levitation force, which increases with increasing height or thickness of the rings.This paper presents an analysis of the magnetic and mechanical properties of arrays of superconducting rings arranged in axial, radial, and matrix configurations under different magnetic fields. In terms of the Bean's critical state model and the minimum magnetic energy method, the dependences of the magnetization and levitation behaviors on the geometry, number, and gap of the superconducting rings are obtained. The results show that when the applied field is spatially uniform, the magnetic property of the superconducting array is associated with the gaps between the rings. For the case of small gaps, the entire array becomes not easy to be fully penetrated by the induced currents, and the magnetic field profiles of which are almost the same as ones in a single large ring. If the superconducting array is fully penetrated, its saturation magnetization value is affected by the radial interval and, however, is almost independent of the vertical separation. When the applied field produced by a cylindrical permanent magnet is nonuniform, the superconducting array will be subjected to a levitation force. The levitation force increases monotonically and finally reaches a saturation value with increasing height or thickness of the rings, and such saturation value is closely related to the inner radius of the array.

The transient anti-plane problem of a magnetoelectroelastic strip containing a crack vertical to the boundary is considered. Singular integral equations for the impermeable crack are obtained by using Fourier and Laplace transforms. Numerical results show the effects of the relative loading parameters κD and κB, and the crack configuration on the dynamic fracture behavior. The results obtained indicate that for the impermeable crack, the electric and magnetic impacts have significant influences on the dynamic stress intensity factor and the dynamic energy density factor.

This letter presents a theoretical model of the normal (head-on) collisions between two soft spheres for predicting the experimental characteristic of the coefficient of restitution dependent on impact velocity. After the contact force law between the contacted spheres during a collision is phenomenologically formulated in terms of the compression or overlap displacement under consideration of an elastic—plastic loading and a plastic unloading subprocesses, the coefficient of restitution is gained by the dynamic equation of the contact process once an initial impact velocity is input. It is found that the theoretical predictions of the coefficient of restitution varying with the impact velocity are well in agreement with the existing experimental characteristics which are fitted by the explicit formula.

This paper presents a theoretical model on the normal (head-on) collision between soft-spheres on the basis of elastic loading of the Hertz contact for compression process and a nonlinear plastic unloading for restitution one, in which the parameters all are determined in terms of the material and geometric ones of the spheres, and the behaviors of perfect elastic, inelastic, and perfect plastic collisions appeared in the classical mechanics are fully described once a value of coefficient of restitution is specified in the region of 0 ≤ ε ≤ 1. After an empirical formula of the coefficient of restitution dependent on the impact velocity is suggested to fit the existing experimental measurements by means of the least square method, the predictions of the dependency and the collision duration are in well quantitative agreement with their experimental measurements. It is found that the measurable quantities are dependent on both the impact velocity and the parameters of spheres. Following this model, finally, an approach to determine the spring coefficient in the linear viscoelastic model of the collision is also displayed. These results obtained here will be significantly beneficial for the applications where a collision model is requested in the simulations of relevant grain flows and impact dynamics etc..

This paper mainly reports an improvement of frozen-image model which can qualitatively describe the influence of lateral moving speed on vertical force in a HTS levitation system under lateral movement with field-cooling condition. The model is improved by introducing a dipole which represents the influence of lateral moving speed and modifying the rule of diamagnetic dipole based on frozen-image model. The vertical and lateral forces that are obtained by this improved model agree with the previous measurements qualitatively. This model can also describe the effect of finite scale of superconductor sample in a levitation system.