固体电介质中的挠曲电效应

挠曲电效应通常描述为非均匀变形如应变梯度引起的电极化或者电场梯度引起的变形.应变梯度能够局部破坏晶体的反演对称从而在材料中诱导电极化,因此挠曲电效应是固体电介质材料中普遍存在的一种力电耦合效应.应变梯度和电场梯度均随材料尺寸的减小而迅速增大,在宏观尺度通常被忽略的挠曲电效应在微纳尺度反而起着非常重要的作用,会显著影响材料的物理性能.与压电效应和电致伸缩效应相比,挠曲电效应具有独特的尺寸依赖特征,其不受材料对称性和铁电材料居里相变温度的限制.论文综述了固体电介质中的挠曲电效应,并重点从理论、材料和应用方面综述了固体电介质中挠曲电效应的研究进展,对挠曲电效应的独特性能进行了详细地讨论,最后论文展望了固体电介质中挠曲电效应相关研究的开放性问题和发展方向.     

晶体位错尺寸效应的多尺度分析

本文采用准连续介质多尺度方法,分析了面心立方（fcc）晶体铝阶梯孪晶界在不同尺寸情况下（试件尺寸长高比从1：1到8：1）受剪切作用的晶界变形。了解在不同尺寸下,晶界结构位错的成核过程,得到了大试件比值与小试件比值下作用力与应变的关系曲线及不同试件尺寸下应变能的变化曲线。其中随着试件比值的增加,作用力在应变比较小的时候变化情况相似,但当应变达到3％以后,呈现出明显的不同;应变能随试件长高比的增大而减小,各个试件在各自不同的加载阶段,应变能变化趋势同作用力变化趋势相一致。本计算揭示了不同尺寸下阶梯孪晶界在剪切作用下的微观机理,证实其尺寸效应性质。     

基于广义应变梯度理论的纳米梁挠曲电效应研究

挠曲电效应是应变梯度与电极化的耦合,它存在于所有的电介质材料中。在纳米电介质结构的挠曲电效应研究中,应变梯度弹性对挠曲电响应的影响一直以来被低估甚至被忽略了。根据广义应变梯度理论,应变梯度弹性中独立的尺度参数只有三个,而文献中所采用的一个或两个尺度参数的应变梯度理论只是它的简化形式。基于该理论,论文建立了考虑广义应变梯度弹性的三维电介质结构的理论模型,并以一维纳米梁为例研究了其弯曲问题的挠曲电响应及其能量俘获特性。结果表明,纳米梁的挠曲电响应存在尺寸效应,并且弹性应变梯度会影响结构挠曲电的尺寸效应,特别是当结构的特征尺寸低于尺度参数时。论文的工作为更进一步理解纳米尺度下的挠曲电机理和能量俘获特性提供理论基础和设计依据。     

基于虚内键理论的材料多尺度力学模型

宏观上线弹性材料的力学属性只需杨氏模量和泊松比两个相互独立的参量来控制;相应地,微观上也需要两个相互独立的参量来控制.基于这个思想,在原VIB模型中引入了切向键,并提出了VMIB模型.该模型在材料的宏观力学属性与微观虚拟键力学属性之间建立起了一座桥梁.考虑到模型中能量密度函数含有坐标轴方向向量一项,该文对能量密度函数的张量性进行了严格的数学证明,并将VMIB模型初步应用到脆性材料的单轴受压破坏.     

变分多尺度方法在一维力学模型中的应用

将变分多尺度方法应用于一维缆索模型,导出受力缆索的宏观有限元模型并求得细观位移解析解,总结出变分多尺度方法应用于具体模型的关键点和缺陷. 假定刚度为常值,数值模拟一定边界和受力下的缆索,得到宏观和细观位移. 将细观与宏观位移叠加,相比于精确位移得出：细观位移可视为常规有限元模型的后验误差. 变分多尺度方法在一维力学模型中的成功应用,推进了其实用性,为其在更多力学及工程问题中的运用和发展提供了参考.     

Defects in flexoelectric solids

A solid is said to be flexoelectric when it polarizes in proportion to strain gradients. Since strain gradients are large near defects, we expect the flexoelectric effect to be prominent there and decay away at distances much larger than a flexoelectric length scale. Here, we quantify this expectation by computing displacement, stress and polarization fields near defects in flexoelectric solids. For point defects we recover some well known results from strain gradient elasticity and non-local piezoelectric theories, but with different length scales in the final expressions. For edge dislocations we show that the electric potential is a maximum in the vicinity of the dislocation core. We also estimate the polarized line charge density of an edge dislocation in an isotropic flexoelectric solid which is in agreement with some measurements in ice. We perform an asymptotic analysis of the crack tip fields in flexoelectric solids and show that our results share some features from solutions in strain gradient elasticity and piezoelectricity. We also compute the energy release rate for cracks using simple crack face boundary conditions and use them in classical criteria for crack growth to make predictions. Our analysis can serve as a starting point for more sophisticated analytic and computational treatments of defects in flexoelectric solids which are gaining increasing prominence in the field of nanoscience and nanotechnology.     

基于多尺度网格细胞模型的无人机类脑矢量导航方法

动物具有优秀的矢量导航能力,为发展未知环境下无人机新型自主智能面向目标导航方法提供了较好的生物模型。首先阐述了动物大脑矢量导航机理,然后重点研究了多尺度网格细胞模块编码与解码机制,提出一种大尺度空间下基于多尺度网格细胞模型的无人机类脑矢量导航方法。通过在多个吸引子神经网络中引入指数递增型速度增益因子,提出了多尺度网格细胞路径积分方法(编码);基于余数系统框架提出了大尺度空间网格细胞矢量导航解算方法(解码)。仿真实验结果表明:所提方法能够适应在最大范围38km的大尺度空间中对速度、方位信息进行准确多尺度路径积分(编码),并准确解算当前距目标矢量(解码);验证了所提方法能够进行大尺度空间矢量导航,对进一步发展大尺度空间下无人机三维类脑矢量导航方法具有较好的参考意义。     

Size-dependent electromechanical properties in piezoelectric superlattices due to flexoelectric effect

Piezoelectric superlattice is a potential component for nanoelectromechanical systems.Due to the strong nonlocal effect such as flexoelectric effect at interfaces,classical piezoelectric theory is unable to accurately describe the electromechanical response of piezoelectric superlattice at nanoscale scale.Based on the previous nonlocal thermodynamics theory with flexoelectric effect Liu et al.(2016),the sizedependent electromechanical properties of piezoelectric superlattices made of BaTiO_3(BTO)and PbTiO_3(PTO)layers are investigated systematically in the present work.Giant strain gradient is found near the interface between BTO and PTO layers,which leads to the significant enhancement of polarization in the superlattice due to the flexoelectric effect.For the piezoelectric BTO–PTO superlattices with different unitcell sizes,the thickness of interface with nontrivial strain gradient is almost constant.The influence of strain gradient at the interface becomes significant when the size of superlattice decreases.As a result,a strong size dependence of electromechanical properties is predicted for the piezoelectric BTO–PTO superlattices.In particular,for the superlattices with a specific thickness ratio of BTO and PTO layers,the piezoelectric response can be several times larger than that of bulk structure.The present work demonstrates a practical way to design the piezoelectric superlattices with high piezoelectric coefficient by using the nonlocal effect at nanoscale.     

Vibration analysis of periodic cellular solids based on an effective couple-stress continuum model

Cellular solids are usually treated as homogeneous continuums with effective properties. Nevertheless, these mechanical properties depend strongly on the ratio of the specimen size to the cell size. These size effects may be accounted for according to preliminary static analysis of effective continuums based on couple-stress theory. In this paper an effective dynamic continuum model, based on couple-stress theory, is proposed to analyze the behavior of free vibrations of periodic cellular solids. In this continuum model, the effective mechanical constants of the effective continuum are deduced by an equivalent energy method. The cellular solid structure is then replaced with the equivalent couple-stress continuum with same overall dimension and shape. Moreover, the finite element formulation of the couple-stress continuum for the generalized eigenvalue analysis is developed to implement the free vibration analysis. The eigenfrequencies of the effective continuum are then obtained via the shear beam theory or the finite element method. A conventional finite element analysis by discretizing each cell of the cellular solids is also carried out to serve as an exact solution. Several structural cases are calculated to demonstrate the accuracy and effectiveness of the proposed continuum model. Good agreement on structural eigenfrequencies between the effective continuum solutions and the exact solutions shows that the proposed continuum model can accurately simulate the dynamic behavior of the cellular solids.     

悬臂梁挠曲电俘能器的力电耦合模型及性能分析

挠曲电效应指应变梯度在电介质中引起的电极化现象,是一种普遍存在的力电耦合行为。应变梯度与材料的尺寸成反比,因此挠曲电效应有望在纳米尺度主导材料的物理性质,尤其是力电耦合性能。本文建立了悬臂梁挠曲电俘能器的理论模型,基于哈密顿原理得到了悬臂梁挠曲电俘能器的控制方程和相应的边界条件;进一步,得到了悬臂梁挠曲电俘能器的输出电压频率响应和功率密度频率响应随悬臂梁的振动频率、外电路阻抗、挠曲电层厚度以及弹性层模量的变化规律。聚偏氟乙烯和环氧树脂层合挠曲电悬臂梁俘能器模型的数值结果表明输出电压频率响应和功率密度频率响应在共振频率点取得最大值,且随着各阶模态对应的共振频率的增加悬臂梁挠曲电俘能器的输出电压和功率密度均增加。此外,计算结果还表明悬臂梁俘能器存在最佳匹配阻抗,在匹配阻抗附近悬臂梁俘能器的输出功率密度随挠曲电层厚度的减小而增大,表现出明显的尺寸效应。本文工作提供了一种基于挠曲电效应的悬臂梁俘能器的理论模型,为悬臂梁俘能器的设计提供了理论依据。     

悬臂梁挠曲电俘能器的力电耦合模型及性能分析

挠曲电效应指应变梯度在电介质中引起的电极化现象,是一种普遍存在的力电耦合行为。应变梯度与材料的尺寸成反比,因此挠曲电效应有望在纳米尺度主导材料的物理性质,尤其是力电耦合性能。本文建立了悬臂梁挠曲电俘能器的理论模型,基于哈密顿原理得到了悬臂梁挠曲电俘能器的控制方程和相应的边界条件;进一步,得到了悬臂梁挠曲电俘能器的输出电压频率响应和功率密度频率响应随悬臂梁的振动频率、外电路阻抗、挠曲电层厚度以及弹性层模量的变化规律。聚偏氟乙烯和环氧树脂层合挠曲电悬臂梁俘能器模型的数值结果表明输出电压频率响应和功率密度频率响应在共振频率点取得最大值,且随着各阶模态对应的共振频率的增加悬臂梁挠曲电俘能器的输出电压和功率密度均增加。此外,计算结果还表明悬臂梁俘能器存在最佳匹配阻抗,在匹配阻抗附近悬臂梁俘能器的输出功率密度随挠曲电层厚度的减小而增大,表现出明显的尺寸效应。本文工作提供了一种基于挠曲电效应的悬臂梁俘能器的理论模型,为悬臂梁俘能器的设计提供了理论依据。     

Domain switching effect on fracture of piezoelectric solids

Rational design of smart sensors and actuators that consist of piezoelectric solids requires a thorough understanding of the constitutive behavior of this material under mechanical and electrical loading. Domain switching is the cause of significant nonlinearity in the constitutive behavior of piezoelectric solids, which may be enhanced in the presence of cracks. In this paper, the response of piezoelectric solids is formulated by coupling thermal, electrical, and mechanical effects. The corresponding finite element equations are derived and applied in the solution of the piezoelectric center crack problems. The effects of domain switching are evaluated on the near tip stress intensity factors.     

SIZE EFFECT AND GEOMETRICAL EFFECT OF SOLIDS IN MICRO—INDENTATION TEST

Micro-indentation tests at scales of the order of sub-micron show that the measured hardness increases strongly with decreasing indent depth or indent size,which is frequently referred to as the size effect.At the same time,at micron or sub-micron scale,another effect,which is referred to as the geometrical size effects such as crystal grain size effect,thin flim thickness effect,etc.,also influences the measured material hardness.However,the trends are at odds with the size-independence implied by the conventional elastic-plastic theory.In the present research,the strain gradient plasticity theory(Fleck and Hutchinson)is used to model the composition effects(size effect and geometrical effect) for polycrystal material and metal thin film/ceramic substrate systems when materials undergo micro-indenting.The phenomena of the “pile-up“ and “sink-in“ apeared in the indentation test for the polycrystal materials are also discussed.Meanwhile,the micro-indentation experiments for the polycrystal Al and for the Ti/Si3N4 thin film/substrate system are carried out.By comparing the theoretical predictions with experimental measuremtns.the values and the variation trends of the micro-scale parameter included in the strain gradient plasticity theory are predicted.