力电耦合偏场理论:回顾、比较与展望

力电耦合固体的非线性连续介质理论最早出现于20世纪50年代,而成熟于70年代.80年代末、90年代初则因智能材料与结构的兴起而又得到了新的发展,引起了较为广泛的关注,但应用上以线性分析为主.21世纪初以来,力电耦合软材料因其潜在的应用前景激发了众多的研究兴趣.由于牵涉到大变形,必须在一般非线性连续介质力学的框架内进行问题的建模和开展定量分析,因此力电耦合固体的非线性理论重新得到了大家的重视,出现了很多新版本.本文旨在阐述力电耦合固体非线性连续介质理论一般框架的基础上,采用3个构型的表述方式,较为详细地给出拉格朗日描述和更新拉格朗日描述下的力电耦合偏场理论,甄别不同理论表述版本之间的异同,以廓清目前文献中的混乱现象,为今后的相关研究提供理论指导.最后,本文讨论和展望了力电耦合偏场理论在不同研究领域的若干研究重点及其未来发展趋势.     

铁电复合材料的力电耦合行为

对铁电复合材料力电耦合行为的研究进行综述．介绍了铁电复合材料的一些基本特点和线性压电有效性能的研究进展．阐述铁电复合材料中由于铁电相的铁电畴变与铁弹畴变以及基体相的弹性、粘弹性和介电弛豫性质所引起的铁电复合材料的非线性力电耦合行为．介绍了基于细观力学方法对铁电复合材料的本构关系进行研究的一些结果．     

电弹性体力学中的偏场方法及其应用

主要综述了当前有关叠加于偏场之上的电弹性体小位移问题的求解方法,即偏场方法.首先介绍了作为偏场方法理论基础的非线性电弹性力学理论,接着总结了偏场方法的研究进展以及受偏场作用后,电弹性梁、板、壳结构的分析方法,随后综述了偏场方法的诸多应用:其中,包括在薄壁电弹性结构屈曲分析中的应用、在记时与通信压电谐振器和基于频率漂移原理所设计的声波传感器的频率稳定性分析方面的应用、在非线性电弹性材料系数的测定以及偏场作用下电致伸缩陶瓷特征的分析等方面的应用.最后给出了该领域当前和未来的一些可能的研究课题.全文参考文献166篇.      

理论力学研究性教学新探索: 刚体运动基点法公式与连续介质速度场分解

基础力学课程体系是现代工程教育的重要基础。理论力学作为力学课程体系的起点,提供了力学基本概念和原理。一方面,以离散体系(质点/刚体)为研究对象的理论力学与以连续体系(介质/变形微元体)为对象的连续介质力学,它们之间既存在密切联系又差异明显;另一方面,源于理论/经典力学的动力系统理论和非线性科学研究对应用力学学科产生了广泛影响。围绕这两个侧面,作者将在《理论力学研究性教学新探索》系列教研论文中阐释它们之间的联系。本篇探讨刚体运动基点法公式和连续介质速度场分解之间的关系,它们分别给出刚体模型和连续介质模型的速度分布规律,前者依赖刚体转动角速度矢量,而后者由速度梯度张量所刻画。本文将说明,两者存在对应理论关系,且刚体基点法公式是连续介质速度场分解的退化形式,即忽略变形效应。

     

摄动理论在求解流固耦合渗流问题中的应用

通过引进小参数ε，对工程中一类强非线性耦合渗流问题采用摄动理论进行解析求解，探讨了数学模型中压力动态分布特征，并通过数值算例分析了压力随饱和度s及时间t变化的情况，可为实验确定压力-饱和度-渗透率之间的关系提供理论依据，同时为求解非线性偏微分数学方程组提供一种解析求解方法．     

多物理场耦合作用分析的近场动力学理论与方法

广义来说, 近场动力学(peri-dynamics,PD)是假设每个物质点在承受一定范围内的非接触相互作用下,研究整个物理系统演化过程的理论,为涉及非连续和非局部相互作用的问题提供了一个统一的数学框架,具有广泛的适用性.在简要介绍诸多工程对于多物理场模型和数值计算软件的迫切需求后,针对现有商用软件在处理结构非连续演化问题时遇到的瓶颈,引入近场动力学理论和方法. 概述近场动力学固体力学模型,系统阐述近场动力学扩散模型和近场动力学多物理场耦合建模的研究现状和进展,主要涉及电子元器件、电子封装和岩土工程领域的多物理场耦合建模,包括热--力、湿--热--力、热--氧、热--力--氧、力--电、热--电、力--热--电、多孔介质的水--力流固相互作用等非耦合、半耦合与完全耦合模型,强调发展耦合方程数值解法的重要性.最后对扩散问题和多物理场耦合问题的近场动力学理论模型、数值算法和工程应用做进一步展望.      

一种化学-力学耦合连续介质理论与数值格式

对化学驱动的连续介质化学-力学耦合系统进行研究,从热力学定律和化学势角度出发,推导了等温过程的化学-力学耦合本构关系和控制方程,利用变分方法建立了化学-力学耦合系统的能量泛函,得到化学-力学耦合控制方程的等效积分形式和相应的有限元列式. 结合算例,对连续介质的化学-力学耦合行为进行了数值计算,数值结果反映了化学与力学系统的相互耦合作用,即浓度变化能引起介质的变形,同样力学作用也能引起浓度重分布. 从全新的角度建立了描述连续介质的化学-力学耦合行为的基本理论和数值方法,能够较好地反映一类连续介质的化学-力学耦合行为.      

水凝胶多场耦合计算力学

作为一种具有多场耦合特性的智能柔体材料,水凝胶的制备技术、性能表征与结构应用得到迅速发展。本文在分析水凝胶本构理论和结构设计的基础上,提出了水凝胶多场耦合计算力学的基本方法和范式,包括微观粗粒化分子动力学模拟和宏观耦合有限元方法等,计算了化学-力学耦合作用下水凝胶材料与结构的变形和应力,给出了多个数值算例与结果比较。研究指出多场耦合计算力学将成为水凝胶材料和结构分析的主要手段,并推动水凝胶等这类智柔材料的性能设计与工程应用。     

基于场分离的水下爆炸流固耦合计算方法

基于谱单元方法对水下爆炸流固耦合机理进行了研究,针对总场模型中入射波在流体网格中传播会产生失真现象的问题,采用场分离技术,通过理论推导建立了水下爆炸流固耦合问题的散射场数值模型.经过编程计算比较得出,散射场数值模型有效解决了入射波在流体网格中传播的失真问题,比总场模型计算精度更高,可较好地应用于水下爆炸流固耦合问题的求...     

非定常流场降阶模型及其应用研究进展与展望

非定常流场模型降阶技术的出现,为CFD／CSD耦合数值模拟方法在工程设计中的广泛应用提供了新机遇．在对非线性系统模型降阶理论与方法进行概述的基础上,全面系统地介绍了非定常流场降阶模型的国内外研究进展．按基于系统辨识的降阶模型和基于流场特征结构的降阶模型两大类进行评述,比较了各种降阶模型的优缺点并指出了进一步改进的思路．...     

Theory of electroelasticity accounting for biasing fields: Retrospect,comparison and perspective

力电耦合固体的非线性连续介质理论最早出现于20世纪50年代,而成熟于70年代.80年代末、90年代初则因智能材料与结构的兴起而又得到了新的发展,引起了较为广泛的关注,但应用上以线性分析为主.21世纪初以来,力电耦合软材料因其潜在的应用前景激发了众多的研究兴趣.由于牵涉到大变形,必须在一般非线性连续介质力学的框架内进行问题的建模和开展定量分析,因此力电耦合固体的非线性理论重新得到了大家的重视,出现了很多新版本.本文旨在阐述力电耦合固体非线性连续介质理论一般框架的基础上,采用3个构型的表述方式,较为详细地给出拉格朗日描述和更新拉格朗日描述下的力电耦合偏场理论,甄别不同理论表述版本之间的异同,以廓清目前文献中的混乱现象,为今后的相关研究提供理论指导.最后,本文讨论和展望了力电耦合偏场理论在不同研究领域的若干研究重点及其未来发展趋势.     

Higher order fields for damaged nonlinear antiplane shear notch, crack and inclusion problems

Damaged nonlinear antiplane shear problems with a variety of singularities are studied analytically. A deformation plasticity theory coupled with damage is employed in analysis. The effect of microscopic damage is considered in terms of continuum damage mechanics approach. An exact solution for the general damaged nonlinear singular antiplane shear problem is derived in the stress plane by means of a hodograph transformation, then corresponding higher order asymptotic solutions are obtained by reversing the stress plane solution to the physical plane. As example, traction free sharp notch and crack, rigid sharp wedge and flat inclusion, and mixed boundary sharp notch problems are investigated, respectively. Consequently, higher order fields are obtained, in which analytical expressions of the dominant and second order singularity exponents and angular distribution functions of the near tip fields are derived. Effects of the damage and hardening exponents of materials and the geometric angle of notch/wedge on the near tip quantities are discussed in detail. It is found that damage leads to a weaker dominant singularity of stress, but to little stronger singularities of the dominant and second order terms of strain compared to that for undamaged material. It is also seen that damage has important effect on the angular distribution functions of the near tip stress and strain fields. As special cases, higher order analytical solutions of the crack and rigid flat inclusion tip fields are obtained, respectively, by reducing the notch/wedge tip solutions. Effects of damage and hardening exponents on the dominant and second order terms in the solutions of the crack and inclusion tip fields are discussed.     

Quadratically Nonlinear Cylindrical Hyperelastic Waves: Derivation of Wave Equations for Axisymmetric and Other States

A rigorous approach of nonlinear continuum mechanics is used to derive nonlinear wave equations that describe the propagation and interaction of hyperelastic cylindrical waves. Nonlinearity is introduced by means of metric coefficients, the Cauchy—Green strain tensor, and the Murnaghan potential and corresponds to the quadratic nonlinearity of all basic relationships. Quadratically nonlinear wave equations are derived for three states (configurations): (i) axisymmetric configuration dependent on the radial and axial coordinates and independent of the angular coordinate, (ii) configuration dependent on the angular coordinate, and (iii) axisymmetric configuration dependent on the radial coordinate. Four ways of introducing physical and geometrical nonlinearities to the wave equations are analyzed. Six different systems of wave equations are written __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 72–84, June 2005.     

Quadratically Nonlinear Cylindrical Hyperelastic Waves: Derivation of Wave Equations for Plane-Strain State

A method is proposed for deriving nonlinear wave equations that describe the propagation and interaction of hyperelastic cylindrical waves. The method is based on a rigorous approach of nonlinear continuum mechanics. Nonlinearity is introduced by means of metric coefficients, Cauchy-Green strain tensor, and Murnaghan potential and corresponds to the quadratic nonlinearity of all basic relationships. For a configuration (state) dependent on the radial and angle coordinates and independent of the axial coordinate, quadratically nonlinear wave equations for stresses are derived and stress-strain relationships are established. Four ways of introducing physical and geometrical nonlinearities to the wave equations are analyzed. For one of the ways, the nonlinear wave equations are written explicitly__________Translated from Prikladnaya Mekhanika,Vol. 41, No. 5, pp. 40–51, May 2005.     

超空泡射弹尾拍分析与计算

对超空泡射弹进行运动学和动力学分析并数学建模,求解耦合非线性微分方程组,得到水下高速超空泡射弹运动特性。数值模拟结果表明,高速超空泡射弹在航行过程中,由于弹体头部和尾部的阻力作用,水平速度随时间迅速衰减。并且射弹的角速度呈周期性往复变化,即尾拍现象。同时由于空泡尺寸的减小导致尾拍幅度逐渐变小。射弹转动惯量越小,角速度变化幅度越平稳,相同时间内尾拍次数减少。发射深度或发射速度越大,尾拍幅度衰减越快。较大的初始角速度也会使射弹角速度很快衰减。     

材料生长与变形的连续介质模型:平衡方程与边界条件

本文探讨了生长变形体连续介质模型的平衡理论框架。文中首先证明了广义输运定理，根据这个定理，推导了生长变形体广义平衡方程的一般形式及其生长边界条件，并导出反映生长边界面对平衡影响的生长耦合函数。在此基础上，具体讨论了质量、动量、动量矩以及能量平衡方程，并对其中相伴出现的一些新的物理量进行了评述；此外，还根据非平衡热力学理论的局域平衡假设建立了描述生长变形体热力学过程的熵不等式。这些方程唯象反映了生长变形体在运动、变形与生长过程中各物理量之间的耦合关系与平衡规律。     

Rheometry for large-particulated fluids: analysis of the ball measuring system and comparison to debris flow rheometry

For large-particulated fluids encountered in natural debris flow, building materials, and sewage treatment, only a few rheometers exist that allow the determination of yield stress and viscosity. In the present investigation, we focus on the rheometrical analysis of the ball measuring system as a suitable tool to measure the rheology of particulated fluids up to grain sizes of 10 mm. The ball measuring system consists of a sphere that is dragged through a sample volume of approximately 0.5 l. Implemented in a standard rheometer, torques exerted on the sphere and the corresponding rotational speeds are recorded within a wide measuring range. In the second part of this investigation, six rheometric devices to determine flow curve and yield stress of fluids containing large particles with maximum grain sizes of 1 to 25 mm are compared, considering both rheological data and application in practical use. The large-scale rheometer of Coussot and Piau, the building material learning viscometer of Wallevik and Gjorv, and the ball measuring system were used for the flow curve determination and a capillary rheometer, the inclined plane test, and the slump test were used for the yield stress determination. For different coarse and concentrated sediment–water mixtures, the flow curves and the yield stresses agree well, except for the capillary rheometer, which exhibits much larger yield stress values. Differences are also noted in the measuring range of the different devices, as well as for the required sample volume that is crucial for application.     

Non Linear Rheology for Long Chain Branching characterization,comparison of two methodologies : Fourier Transform Rheology and Relaxation.

In this study we compare three rheological ways for Long Chain Branching (LCB) characterization of a broad variety of linear and branched polyethylene compounds. One method is based on dynamical spectrometry in the linear domain and uses the van Gurp Palmen plot. The two other methods are both based on non linear rheology (Fourier Transform Rheology (FTR) and chain orientation/relaxation experiments). FTR consists in the Fourier analysis of the shear stress signal due to large oscillatory shear strains. In the present work we focus on the third and the fifth harmonics of the shear stress response. Chain orientation/relaxation experiment consists in the analysis of the polymer relaxation after a large step strain obtained by squeeze flow. In this method, relaxation is measured by dynamical spectrometry and is characterized by two relaxation times related to LCB. All methods distinguish clearly the group of linear polyethylene from the group of branched polyethylene. However, FTR and Chain orientation/relaxation experiments show a better sensitivity than the van Gurp Palmen plot. Non linear experiments seem suitable to distinguish long branched polyethylene between themselves.