Flux-Pinning-Induced Stress and Deformation Analyses of a Long Rectangular Superconducting Bicrystal

The flux-pinning-induced stress and deformation of a long rectangular superconducting bicrystal with an arbitrary aspect ratio are analyzed based on the critical-state model and the finite element numerical method. The flux and current distributions in the superconductor with a low-angle grain boundary (GB) are obtained based on a constant GB critical current density assumption. The distributions of the stresses within the superconductor are obtained for different magnetization stages. The deformation and especially the shape distortion in the irreversible magnetostriction of the superconductor are analyzed. In addition, the relation between the maximum stress on the grain boundary and the ratio of the GB critical current density to the grain critical current density is discussed when the applied magnetic field is reduced to zero.     

The Nature of Stress and Electric-displacement Concentrations around a Strongly Oblate Cavity in a Transversely Isotropic Piezoelectric Material

In this paper we explore the nature of stress and electric-displacement concentrations around a strongly oblate spheroidal cavity that possesses a finite dielectric permittivity. We start out from Eshelby’s general inclusion method but give specific account on the important class of piezoelectric ceramics whose structure is represented by the 6 mm symmetry. It is found that under axial electromechanical loading these concentrations are governed by a dimensionless parameter η, defined as (k₀/k₃₃)/(c/a), that involves the ratio of the dielectric permittivity of the medium inside the cavity k₀, to that of the transversely isotropic piezoelectric ceramic k₃₃, and the aspect ratio of the cavity c/a. When the medium inside the cavity is an impermeable one it is found that both the axial stress and axial electric displacement can have direct contribution to the concentration factors, but when the medium is a conducting one only the applied stress has an effect on it. Our analysis further indicates that it is the parameter η – not k₀/k₃₃ or c/a alone – that plays the key role here; when η< 0.01, the cavity can be effectively treated as an impermeable one, while for η> 100 it can be treated as a conducting case. Numerical results for several PZT ceramics suggest that under a pure tensile stress the ceramic tends to fracture on the equatorial plane, but under a pure electrostatic load it tends to develop radial cracks normal to the edge of the cavity.     

Healing of an Internal Plane Crack in a Transversely Isotropic Body

Materials Science - We propose a mathematical model of healing of a crack located in the plane of isotropy of a transversely isotropic body subjected to the action of arbitrary external loads...     

Limiting State of Transversely Isotropic Plates with Surface and Internal Cracks

We propose a method for the analysis of the limiting state of transversely isotropic plates with surface and internal cracks and obtain a new simple approximate formula for the evaluation of the stress intensity factors. The numerical calculations are based on the improved version of the analysis of stress-strain states in defect-free transversely isotropic plates. The failure is initiated as soon the damage ratio near the crack front in the direction of crack propagation attains a certain critical value.     

Comparison of Alternative Techniques for Characterizing Magnetostriction and Inverse Magnetostriction in Magnetic Thin Films

We compare the direct and inverse techniques of measuring magnetostriction in magnetic thin films. We chose a set of four magnetic thin film samples (Co$_{95}$Fe$_5$, Co$_{60}$Fe$_{20}$B$_{20}$, Ni$_{65}$Fe$_{15}$Co$_{20}$, and Ni$_{80}$Fe$_{20}$) for the measurements, representing positive and negative magnetostriction and having saturation magnetostriction of magnitudes ranging from $10^{-7}$ to $10^{-5}$. We made the direct measurements on a high-precision optical cantilever beam system, and we carried out the inverse magnetostriction measurements on a nondestructive inductive $Bhbox{-}H$ looper with three-point bending stage.      

Magnetization of a Current-Carrying Superconducting Disk with B-Dependent Critical Current Density

In the frame work of the critical state model (CSM), the magnetic response of a thin type-II superconducting disk that carries a radial transport current and is subjected to an applied magnetic field have been studied. To this end, we have studied the process of the magnetic flux-penetration. For a disk initially containing no magnetic flux but carrying a radial current, when a perpendicular magnetic field is applied, magnetic flux-penetration occurs in three stages: (1) the magnetic flux gradually penetrates from the edges of the disk until an instability occurs, (2) there is a rapid inflow of magnetic flux into the disk’s central region, which becomes resistive, and (3) magnetic flux continues to enter the disk, while persistent azimuthal currents flow in an outer annular region where the net current density is equal to J _c . Also the behavior of a current-carrying disk subjected to an AC magnetic field is calculated. The magnetic flux, the current profiles and the magnetization hysteresis loops are calculated for several commonly used J _c (B) dependences. Finally, the results of the applications of the local field-dependent of the critical current density J _c (B) are compared with those obtained from the Bean model.     

Superconducting State of a Disk with a Pentagonal/Hexagonal Trench/Barrier

We study the influence of a pentagonal (hexagonal) trench or barrier on the superconducting properties of a perforated disk. Effects associated to the pinning (anti-pinning) force of the central hole and the trench (barrier) and the interplay between the boundary conditions and the shape of the inner defects on the vortex configuration are studied for a thin disk. Also, we considered two cases for the value of the order parameter at the surface. The first one is ψ _s ≠0; this is the usual supercondutor/vacuum interface, for which the deGennes parameter is b→∞. The second one is ψ _s =0, which is the surface of the sample in a complete normal state, simulated by b=0. The vorticity, Gibbs free energy, magnetic induction, supercurrent density, magnetization and Cooper pairs density as a function of the external magnetic field are calculated. We show that in our sample new phenomena are possible due to the competing interactions of the boundary and the geometry of the sample and the added geometry of the nanoengineered trench and barrier.     

Analysis of Thin Isotropic Rectangular and Circular Plates with Multiquadrics

A computational method based on radial basis functions has been applied to the linear solution of thin plates. This meshless numerical method gives high flexibility in the analysis of irregular geometries, due to its insensivity to spatial dimension. The multiquadrics approach is used in this paper. The numerical solution is compared with Kirchhoff theory for plates.__________Translated from Problemy Prochnosti, No. 2, pp. 72 – 84, March – April, 2005.     

环形凹槽结构借助金属圆盘和金属锥尖实现增强聚束效应

基于传统“牛眼”结构对光波的聚束原理,介绍一种新颖的亚波长光聚束组合结构,在入射端的一定距离添加金属圆盘和出射端添加金属锥尖,实现聚柬能力的增强,FDTD仿真结果表明,基于金属圆盘和金属薄膜之间形成强烈共振的波导腔,使得远场光束中心能量增强 利用金属锥尖对出射光激发的表面等离激元进行局域和收集,抑制了远场光束的边锋,进一步增强了中心光束的能量,角分布变窄。该结构聚束作用和锥尖顶端局域场增强作用可广泛地应用于亚波长光学元器件设计、生物医疗探测等领域。     

Levitation Force Between a Small Magnet and Superconducting Sphere

Based on the Meissner effect and the image method, we studied the interaction between a magnetic point dipole and a superconducting sphere. We obtained analytical expressions for the interaction energy and the levitation force when the dipole is in an arbitrary orientation. Our calculations show the validity of using the image method for a antisymmetrical superconducting sphere-magnet system. Results show that the energy and the force are maxima when the magnetic dipole is perpendicular to the surface of superconductor and minima when it is tangent to the surface. Furthermore, the force acting on the tip of a magnetic force microscope above a superconducting sphere was derived as a generalization of the levitation force acts on a point dipole.      

On a Possible Approximation of Changes in Elastic Properties of a Transversely Isotropic Material due to an Arbitrarily Oriented Crack

The present paper addresses an approximate analytical model for contribution of an arbitrarily oriented circular crack into effective elastic compliance of a transversely isotropic material. We numerically examine the bounds of applicability of the hypothesis that change in elastic potential due to an arbitrarily oriented circular crack in a transversely-isotropic material can be approximated by the change calculated for a certain isotropic environment. In particular, we obtained that the error of such an approximation is less than 20% if the extent of anisotropy is moderate – the ratio of Young’s moduli in transverse and in-plane directions is less than 1.87. The obtained result can be used for development of a simple model for microcracked transversely-isotropic materials with mild-to-moderate extent of anisotropy.     

Effect of Constitutive Parameters on Cavity Formation and Growth in a Class of Incompressible Transversely Isotropic Nonlinearly Elastic Solid Spheres

Cavity formation and growth in a class of incompressible transversely isotropic nonlinearly elastic solid spheres are described as a bifurcation problem, for which the strain energy density is expressed as a nonlinear function of the invariants of the right Cauchy-Green deformation tensor. A bifurcation equation that describes cavity formation and growth is obtained. Some interesting qualitative properties of the bifurcation equation are presented. In particular, cavitated bifurcation is examined for a solid sphere composed of an incompressible anisotropic Gent-Thomas material model with a transversely isotropy about the radial direction. The effect of constitutive parameters on cavity formation and growth is then carried out. It is proved that a cavity forms in the interior of the sphere earlier or later than that in the isotropic Gent-Thomas sphere as the anisotropic parameter takes certain values. The condition for the bifurcation to the left or to the right of the cavity solution is proposed. The stability and the catastrophe of the equilibrium solutions are discussed by using the minimal potential energy principle. Whereas, in contrast to other isotropic nonlinear elastic spheres, cavitated bifurcation in the isotropic Gent-Thomas sphere is quite different, it is proved that the cavity solution can bifurcate locally to the left. The growth of a pre-existing micro-void in the sphere is examined, which interprets the physical implications of the preceding bifurcation problem.     

Nonlinear Dynamical Analysis in Incompressible Transversely Isotropic Nonlinearly Elastic Materials: Cavity Formation and Motion in Solid Spheres

In this paper, the problem of cavity formation and motion in an incompressible transversely isotropic nonlinearly elastic solid sphere, which is subjected to a uniform radial tensile dead load on its surface, is examined in the context of nonlinear elastodynamics. The strain energy density associated with the nonlinearly elastic material may be viewed as the generalized forms of some known material models. It is proved that some determinate conditions must be imposed on the form of the strain energy density such that the surface tensile dead load has a finite critical value. Correspondingly, as the surface tensile dead load exceeds the critical value, a cavity would form in the interior of the sphere and the motion of the formed cavity with time would present a class of singular nonlinear periodic oscillations. The effects of constitutive parameters on cavity formation and motion are discussed in detail, and the corresponding numerical examples are given simultaneously.     

FE Stress Analysis of Thick Composite Laminates with a Hole in Bending

In this work, the stress analysis of isotropic and ortotropic laminae both with a hole and without a hole and laminated both with a hole and without a hole composite plates have been examined using the finite element method. In order to solve the problem, a computer program has been written by using characteristics of eight-node isoparametric plane element. The calculations have been tested on various composite and steel materials by this program. The results have been shown in diagrams and tables and compared with literature. It was observed that the stress distributions in the plate with a hole was totally different from the plate without a hole. The analyses have showed that, the elastic stresses have been gradually reduced as moving from the first layer to the second.     

Spontaneous and Light-Induced Resistive Transitions in Superconducting Thin Film Bridges

In order to study dynamically the resistive states which appear as jumps in the I–V curves of narrow bridges, we have submitted YBaCuO and Nb films to nanosecond current steps and laser pulses simultaneously. In constant current feed, the distinction between hot spots (HS) and phase-slip centers (PSCs) is unambiguous, since HS are compelled to grow or decay, at variance with the stable-in-time PSCs. Thanks to the transient method we show that, even if Joule dissipation associated to a current I is virtually sufficient to sustain the film above T_c, the zero resistance state remains metastable: a hot spot does not arise unless initiated by a PSC, which fact was not reported before. The domains of occurrence of HS and PSCs were then organized in a current–temperature plane. Finally, the theoretical problem of the HS velocity of growth is given an exact solution, in semiquantitative agreement with experiment.     

Analysis of the Dependence of the Range of the Edge Effect in a Laminated Composite with Transversely Isotropic Filler on the Mechanical Characteristics

We study the dependence of the range of the edge effect in a two-component composite with regular structure on the Young moduli and Poisson ratios of the components. The layers filled with a filler and binder are modeled by transversely isotropic and isotropic linearly elastic bodies, respectively. The composite is subjected to the action of a piecewise constant loading applied to the layer of filler. To find approximate solutions of problems in the theory of the edge effect, we use the method of grids based on the concept of basic schemes. We perform an analysis of the accumulated results.     

Multi-vortex State Induced by Proximity Effects in a Small Superconducting Square

The influence of the different negative values of the deGennes parameter \(b\) in the thermodynamic properties of a superconducting infinitely long prism of square cross section area \(S=9\xi ^{2}(0)\) in the presence of a magnetic field is investigated theoretically by solving numerically the nonlinear Ginzburg-Landau equations; \(\xi (0)\) is the coherent length at zero temperature. We obtain the vorticity, magnetic induction, Cooper pair density, magnetization and phase of the order parameter as functions of the external applied magnetic field and the \(b\) parameter. Our results show that a multi-vortex state appear in the sample choosing a convenient value of \(b<0\) parameter, even for such small system. Also, we study a superconducting parallelepiped of volume \(V=Sd\) by means of true \(3D\) numerical simulations; \(d\) is the height of the parallelepiped. We focused our analysis on the way which the magnetization curves approximate from \(d\) finite to the characteristic curve of \(d\rightarrow \infty \) . This is the case for which the magnetic field and the order parameter are invariant along \(z\) -direction. For a superconductor of size \(S=9\xi ^2(0)\) we find that the limit below which the system should be considered a real three-dimensional sample when is \(d=8\xi \) .