Modeling of ferroelectric domains in thin films and superlattices

We have developed the set of numerical (finite-element) and analytical tools that are based on the self-consistent solution of the electrostatic equations coupled with material Ginzburg–Landau equations with an objective to model the profile of domain textures in the entire temperature region. We calculated the evolution of principal parameters of domain texture: modulation vector, distribution of polarization, renormalization of critical temperature etc. In contrast to the Kittel approximation we conclude that the profile of polarization across domains in nanometric ferroelectric thin films is highly nonuniform.     

Irradiated bilayer graphene

We describe the gated bilayer graphene system when it is subjected to intense terahertz frequency electromagnetic radiation. We examine the electron band structure and density of states via exact diagonalization methods within Floquet theory. We find that dynamical states are induced which lead to modification of the band structure. We first examine the situation where there is no external magnetic field. In the unbiased case, dynamical gaps appear in the spectrum which manifest as dips in the density of states. For finite inter-layer bias (where a static gap is present in the band structure of unirradiated bilayer graphene), dynamical states may be induced in the static gap. These states can show a high degree of valley polarization. When the system is placed in a strong magnetic field, the radiation induces coupling between the Landau levels which allows dynamical levels to exist. For strong fields, this means the Landau levels are smeared to form a near-continuum of states.     

Generating radial or azimuthal polarization by axial sampling of circularly polarized vortex beams

A laser beam with circular polarization can be converted into either radial or azimuthal polarization by a microfabricated spiral phase plate and a radial (or azimuthal)-type linear analyzer. The resulting polarization is axially symmetric and is able to produce tightly focused light fields beyond the diffraction limit. We describe in detail the theory behind the technique and the experimental verification of the polarization both in the far field and at the focus of a high numerical aperture lens. Vector properties of the beam under strong focusing conditions were observed by comparing the fluorescence images corresponding to the focal intensity distribution for both radial and azimuthal polarizations. The technique discussed here may easily be implemented to a wide range of optical instruments and devices that require the use of tightly focused light beams.     

Simulation of the initial polarization curves and hysteresis loops for ferroelectric films by an extensive time-dependent Ginzburg–Landau model

The polarization hysteresis loops as well as the initial curves of ferroelectric films with 180° domain boundaries perpendicular to the film surface are simulated based on an extensive time-dependent Ginzburg–Landau model. The result shows that the curve and loop strongly depend on the frequency ω of the applied electric field, the effective mass density ρ, and the viscosity coefficient K of the material, however, the constant ωK/ρ can induce the same curve and loop. The hysteresis area of the saturated loop is increased with field amplitude, which is consistent with the previous experimental observation. In addition, it is found that the latent domains in the film can result in a remarkable decrease in the remanent polarization and coercive field.     

A phenomenological multi-axial constitutive law for switching in polycrystalline ferroelectric ceramics

A phenomenological constitutive law for ferroelectric switching due to multi-axial mechanical and electrical loading of a polycrystalline material is developed. The framework of the law is based on kinematic hardening plasticity theory and has a switching surface in the space of mechanical stress and electric field that determines when non-linear response is possible. The size and shape of the switching surface in a modified electric field space remains fixed during non-linear behavior but its center moves around and thus is controlled by a kinematical hardening process. In general, the remanent polarization and the remanent strain are used as the internal variables that control how the center of the switching surface moves. However, the form presented in this paper has a one-to-one relationship between the remanent strain and the remanent polarization, simplifying the constitutive law and allowing remanent polarization to be used as the only internal variable controlling the kinematic effects. The constitutive law successfully reproduces hysteresis and butterfly loops for ferroelectric ceramics. The hysteresis and butterfly loops respond appropriately to the application of a fixed compressive stress parallel to the electric field. In addition, the law successfully handles remanent polarization rotation due to the application of electric field at an angle to the polarization direction.     

Measurement and analysis of hysteresis torque in a high-speed induction machine

Hysteresis torque is analysed in a high-speed induction machine where the rotor is solid and made of a semihard magnetic material. The hysteresis torque is investigated at first with no load and experimental and numerical methods are considered. The analysis of hysteresis torque is then extended to rated conditions. The numerical modelling is conducted with accurate Preisach hysteresis models coupled with the finite-element method. The hysteresis torque is found to be relatively significant and represents 8% of the rated torque of the studied machine.     

Fourier analysis of thick cross-ply Levy type clamped doubly-curved panels

A hitherto unavailable Levy type analytical solution to the problem of deformation of a finite-dimensional general cross-ply thick doubly-curved panel of rectangular plan-form, modeled using a higher order shear deformation theory (HSDT), is presented. A solution methodology, based on a boundary-discontinuous generalized double Fourier series approach is used to solve a system of five highly coupled linear partial differential equations, generated by the HSDT-based laminated shell analysis, with the C4-type simply supported boundary condition prescribed on two opposite edges, while the remaining two edges are subjected to the SS3-type constraint. The numerical accuracy of the solution is ascertained by studying the convergence characteristics of the deflection and moment of a cross-ply spherical panel, and also by comparison with the available FSDT (first-order shear deformation theory) based analytical solution. Additionally, numerical results pertaining to flat symmetric and antisymmetric cross-ply plates with the same boundary conditions have also been reproduced. Hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to shell geometry (cylindrical and spherical), lamination, lamina material property, and thickness effects, as well as their interactions. Comparison with their SS2 counterparts demonstrates the effect of end clamping on the deflections and moments of thin to thick singly- and doubly-curved cross-ply panels.     

Boundary Conditions at the Bulk–Aerogel Interface of Superfluid 3He-B

We study the interface between bulk and aerogel impregnated with ³ He-B. The magnetic susceptibility at the interface determines a boundary condition for the texture, which can be parameterized by the orbital vector L. We use Ginzburg–Landau theory to calculate the boundary condition assuming homogeneous aerogel and a sharp interface. Recent NMR measurements give reason to conjecture that L tends to be parallel to interface. Our numerical calculations confirm this conjecture in the Ginzburg–Landau (GL) regime. However, the orienting energy is one order of magnitude smaller than at a solid wall, and therefore can easily be overshadowed by a nearby wall.     

A New Approach for Finite-Element Modeling of Hysteresis and Dynamic Effects

Macroscopic behavior of ferromagnetic materials can be considered as the resultant of three phenomena: hysteresis, eddy current, and excess loss. Hysteresis is the behavior of the material under quasi-static variation of magnetic field. Eddy-current and excess losses are dependent on the rate of field variation and are evident in the fast variation of the magnetic field, so they are called dynamic effects. This paper presents a simple and practical technique in field analysis of electromagnetic systems having hysteresis and dynamic effects. Based on the Preisach model for hysteresis and existing formulations for eddy currents and excess loss, an equivalent expression for field intensity has been introduced. A new technique has been presented in order to include this expression in the finite-element code. A typical system has been modeled by this code. Effects of relaxation and time step were examined on the stability and the convergence rate of the method. The validity of the proposed model has been checked by comparing its results with experimental measurements     

Levy type Fourier analysis of thick cross-ply doubly curved panels

A hitherto unavailable Levy type analytical solution to the problem of deformation of a finite-dimensional general cross-ply thick doubly curved panel of rectangular plan-form, modeled using a higher order shear deformation theory (HSDT), is presented. A solution methodology, based on a boundary-discontinuous generalized double Fourier series approach is used to solve a system of five highly coupled linear partial differential equations, generated by the HSDT-based general cross-ply shell analysis, with the SS2-type simply supported boundary condition prescribed on two opposite edges, while the remaining two edges are subjected to the SS3-type constraint. The numerical accuracy of the solution is ascertained by studying the convergence characteristics of deflections and moments of a moderately thick cross-ply spherical panel. Hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to lamination, lamina material property, and thickness and curvature effects, as well as their interactions.     

基于Preisach理论的形状记忆合金温度-位移迟滞仿真研究

摘 要：智能材料如形状记忆合金(Shape Memory Alloy,SMA)已经广泛应用于驱动器和传感器的设计,实现定位和主动控制目的。然而,受迟滞影响,SMA驱动器的工作精度大大降低,限制了其应用。多数智能材料中,选择Preisach理论成为迟滞建模工具,近年来,也涉及到SMA材料系统。本文,讨论运用Preisach模型描述SMA驱动器系统的迟滞行为,尤其针对驱动器系统的模型建立过程,修正经典Preisach模型的几何解释和数值实现方法。最后,引入Gobert给出的Preisach平面的辨识函数执行仿真计算,数值结果表明该模型能够很好地描述SMA驱动器的迟滞行为。     

Birefringence in gradient-index rod lenses: a direct measurement method and interferometric polarization effects

Gradient-index (GRIN) media can contain stress birefringence resulting from the variation in material composition. Anisotropy in a GRIN rod lens affects ray propagation and can degrade image quality. A technique, believed to be new, for measuring birefringence in GRIN rod lenses has been developed. The change in optical path difference (OPD) for orthogonal polarizations is measured directly. With this method, effects on OPD from standard imaging aberrations are excluded. Birefringence measurements for various GRIN rod samples are presented. The data are compared with results obtained previously by use of a Twyman-Green measurement method. Also, the polarization effects on tilt fringes observed with the direct measurement method and the Twyman-Green method are presented and modeled theoretically. Tilt fringes for large birefringence test cases are also modeled.     

An examination of deviations from hydrodynamic penetration theory

The hydrodynamic theory of penetration (HTP) was first developed in the U.S. during WWII, and independently and essentially simultaneously in England. Since then the theory has proved very useful in understanding and predicting results of many penetration experiments. The assumptions and limitations of HTP were well stated in the initial paper. The most obvious limitation is that, strictly speaking, HTP only applies to hydrodynamic materials, i.e., both the projectile and the target have no strength. But for nearly all cases of interest, penetration does depend on material strengths, even at quite high velocities. Consequently, effects of projectile and target strength on penetration physics have been studied by many researchers, and modified versions of HTP have been proposed. While material strength is an important reason for deviations from HTP, it is not the only one. Other assumptions underlying HTP are steady-state behavior and incompressibility. In this paper we present new numerical simulation results that examine and quantify deviations from HTP due to compressibility for several material combinations of interest as a function of impact velocity. For these calculations all the materials are modeled as having zero strength. This is done in order to separate effects of compressibility from effects due to material strength. Some discussion of transient effects is also provided.     

Normally distributed free energy model and creep behavior of ferroelectric polycrystals at room and high temperatures

A constitutive model that can be used to predict creep behavior of ferroelectric polycrystals at room and high temperatures is proposed. The model consists of the Gibbs free energy function with normal distribution and a switching evolution law with critical driving force. Linear moduli in the free energy function and switching parameters in the switching law are assumed to be linearly dependent on temperature. A ferroelectric polycrystal is modeled by an agglomerate of 210 single crystallites. Compressive stress and electric field-induced creep behavior as well as polarization hysteresis and strain butterfly responses of the model are calculated and compared with experimental observations.     

Chaotic and stochastic dynamics for a nonlinear structural system with hysteresis and degradation

In this paper we attempt to introduce some new and fascinating discoveries in chaotic dynamics with particular emphasis on their relationship with stochastic dynamics. Our investigation centers around the deterministic structural system. We begin with a nonlinear hard or soft spring system governed by the well known Duffing's equation. We then add the important engineering material behaviour of hysteresis and degradation. Under a set of unique initial conditions and a harmonic steady-state excitation, the response for a certain deterministic structural system is found to be stochastic.     

Theoretical Investigations of Hysteresis Loops of Ferroelectric or Ferrielectric Nanotubes with Core/Shell Morphology

In this paper, the hysteresis behavior of the nanotubes, consisting of a ferroelectric core of spin-1/2 surrounded by a ferroelectric shell of spin-1/2 with ferro- or anti-ferroelectric interfacial coupling is studied by using the transverse Ising model (TIM). Based on a probability distribution method, the effective field theory has been used to examine the effects of the interfacial coupling constant, the transverse field, and the temperature on the hysteresis loops of the nanotubes. A number of characteristic behaviors have been found, such as the existence of triple hysteresis loops for appropriate values of the system parameters. The remanent polarization and the coercive field, as functions of the temperature, are examined.     

On the numerical simulation of sheet metal blanking process

The use of the blanking process has been widely spread in mass production industries. In this technique, the quality of the final product is directly related to the setting parameters of the process and the material response of the sheet. In the present work, a general framework based on the finite element method for the simulation of the sheet metal blanking process is presented. The proposed approach properly addresses all the numerical challenges related to blanking. First, an extension of elasto-viscoplastic constitutive equations for the large strain regime is used to take into account the material strain-rate sensitivity. Then, the inertial effects coming from high velocity operations are considered by means of an implicit time integration scheme. Moreover, the frictional contact interactions are simulated with the classical Coulomb law and an energetically consistent formulation of area regularization. Finally, ductile fracture is modeled thanks to the element deletion method coupled with a fracture criterion. The blanking process is then simulated for different setting parameters. The accuracy of this approach is evaluated by comparing the numerical predictions to experimental results for both quasi-static and dynamic conditions. Good agreement is found between experimental and numerical results for all cases.     

ON A NUMERICAL METHOD FOR THE EVALUATION OF ELECTROMAGNETIC LOSSES IN ELECTRIC MACHINERY

The paper deals with a numerical method for the evaluation of the magnetic iron losses in steel laminations used in rotating electric machinery. The magnetic hysteresis and the eddy current effects are directly and simultaneously taken into account. Hereby commonly used analytic expressions for the distribution function in the widely adapted Preisach hysteresis model are found to be not quite accurate. The magnetic circuit is decomposed into magnetic and air gap network elements, connected by fundamental loops. The magnetic network elements show a finite element structure. The kinematics of the electric machine is deliberately taken into account by an interpolation technique. Although the model retains the essential features of a cumbersome 3-D problem, a relatively simple algorithm may be developed. For the resulting algebraic system, we propose a suitable decoupling technique, which is efficient from the computational point of view. Numerical experiments show that the results obtained by our numerical approach are in good agreement with the known behaviour of the magnetic material.     

Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals

We present a numerical study of bidimensional photonic crystals with an emphasis on the behavior of the gaps versus the polarization and the conicity of the incident plane wave. We use a rigorous modal theory of diffraction at oblique incidence by a set of arbitrarily shaped parallel fibers. This theory allows the study of the refractive properties of bidimensional photonic crystals. We develop a heuristic method of homogenization that allows us to predict the position of the gaps and their behavior with respect to the polarization and the conicity angle. With this homogenization scheme, we also present some important elements for obtaining full gaps.     

Multiscale modeling of polycrystalline silicon

Polycrystalline solid is composed of randomly distributed grains and grain boundaries. The size of grains is usually in the nano/micro-scale. In this paper, the general micromorphic theory, as well as a specialized micromorphic theory for covalent and ionic crystals, is introduced. A statistical model for polycrystalline material is adopted. Each grain is modeled as crystallized solid by micromorphic theory, while the grain boundaries are modeled as in its amorphous phase by classical continuum theory. Size-dependent material properties of silicon are investigated. Finite element analysis of thermomechanical coupling phenomenon in polycrystalline silicon is performed and numerical results are presented and discussed.