关于非线性基体中Eshelby等效夹杂方法适用性的讨论

本文是对１９９３年力学学报第２５卷第５期“刚性微粒填充的高聚物非线性粘弹性本构关系的微力学分析”的讨论，以远场球对称应力作用下非线性基体中含单个球形刚性粒子或单个球形孔洞为例，给出了问题的精确解．分析表明，关于材料线性的Ｅｓｈｅｌｂｙ等效夹杂方法不能简单地推广应用于研究非线性基体中含刚性粒子或孔洞的力学分析中．     

T应力对立方准晶中含十字交叉型裂纹的影响

论文研究了立方准晶中含十字交叉型裂纹尖端附近的T应力.采用了积分变换法,将相关边值问题转换为求解奇异积分方程,得到声子场和相位子场的T应力,且可以表示为裂纹张开位移和施加在无穷远处的载荷之和.裂纹张开位移在确定声子场和相位子场的T应力中起着主导作用.同时强调了T应力在立方准晶脆性断裂中的作用.此外,还研究了裂纹臂长度比...     

立方晶粒任意集合下的格林函数和有效弹性刚度张量

为了推导多晶体材料的有效弹性刚度张量,给出立方晶粒任意集合的格林函数封闭但近似的表达式,该格林函数表达式包含三个单晶弹性常数和多晶体材料五个织构系数,它考虑取向分布函数的影响直至织构系数的线性项,它适用于弱织构多晶体材料或具有弱各向异性晶粒的多晶体材料(如金属铝),它与Nishioka格林函数近似式的比较通过三个算例给出;Synge的格林函数积分式则直接通过数值计算完成,它可作为问题的精确解供参考.该文还简单介绍了多晶体材料有效弹性刚度张量的推导过程,并把所得结果和有限元计算结果进行比较.     

普通凝固Mg-Zn-Y准晶材料的摩擦磨损特性

采用普通凝固方法制备Mg-Zn-Y准晶材料,在不同试验条件下对普通凝固Mg-Zn-Y准晶材料进行了干摩擦试验,研究了载荷和磨损时间对准晶材料摩擦特性的影响,并对磨损表面形貌及磨屑进行了观察与分析.结果表明:随着载荷的增加,摩擦系数减小;在相同载荷条件下,随着Y含量的增加,摩擦系数及磨损质量损失均逐渐减小,耐磨性逐渐增强.     

变形梯度张量极分解中转动张量的直接表示及其应用

本文通过变分途径建立了变形梯度张量的极分解和加法分解之间的联系.采用工程界通常采用的变形梯度张量的加法分解形式,得到了三维空间中极分解的转动张量和伸长张量的直接表示,即实现了转动和变形的分离.由这些直接表示,可以得到各种有用的近似表示.     

一维正方准晶椭圆孔口平面弹性问题的解析解

利用复变方法,引入广义保角映射,研究了一维正方准晶中具有椭圆孔口的平面弹性问题,给出了各应力分量的复变表示,并在特殊情况下转化为Griffith裂纹,得到该裂纹尖端处的应力强度因子的解析解.当准晶体的对称性增加时,正方准晶椭圆孔口平面弹性问题退化为一维四方准晶中具有椭圆孔口的平面弹性问题,同样在特殊情况下转化为Griffith裂纹,得到裂纹尖端处的应力强度因子的解析解.     

基于椭球曲面拟合的三维磁罗盘误差补偿算法

针对现有三维磁罗盘误差补偿速度慢、需专用转台、野外使用不便的问题,提出了一种建立总磁场的不等边椭球曲面数学模型进行误差补偿的方法.首先根据Poisson方程描述的总磁场测量模型,得出一般椭球曲面模型,然后,采用牛顿迭代法对椭球曲面方程线性化,分别使用最小二乘法和总体最小二乘法计算线性化方程,推导椭球曲面拟合的数学公式,计算椭球曲面参数,最后,利用最小二乘法提出并推导参数初值的计算公式,给出了选取数据点的方法.实验结果表明,仅手持磁罗盘在各象限旋转即可实现误差补偿,航向测量精度可达0.8°,补偿精度与传统的转台补偿基本相同,而补偿方式更为灵活,适用于无转台设备的野外环境测量使用.     

球壳中球形夹杂对SV波的三维散射与动应力集中研究

夹杂将导致结构应力集中,是降低结构承载能力重要影响因素,尤其是动载作用情况下,弹性波衍射和叠加将加剧应力集中程度.弹性波衍射方程建立和求解非常复杂,目前主要研究对象集中在二维模型情况,三维有限域内夹杂引起的动应力集中现象在大型结构中比较常见,有界域边界不仅作为边界条件,同时也是散射波波源,提高了求解难度.一般通过近似方法,将三维模型简化为二维情况,往往导致求解结果过于保守不能解释实际问题.论文针对三维球壳包含夹杂一般情况,分别以球壳和夹杂中心建立球坐标以描述球壳内、外壁和夹杂表面散射波势函数,并引入一种球波函数加法公式实现不同坐标下势函数转换,以求解应力集中状态.最后针对三维情况,给出多个动应力集中因子分布状态以描述动应力集中程度.文中研究为一般情况下含夹杂球壳结构的强度分析提供了理论支撑.     

基于立方型气体状态方程的激波风洞准一维流动数值研究

采用基于立方型气体状态方程的准一维流动数值模拟方法研究了反射式高焓激波风洞的真实气体流动,重点关注了高压真实气体效应对风洞全场流动时空结构和驻室区气流参数的影响,并以理论分析揭示了高压真实气体效应对激波管内流动的作用机理。研究表明：对于以冷高压气体驱动的激波风洞,使用考虑分子体积和分子间作用力的真实气体状态方程能够更准确地描述气体的状态和风洞内的流动状况。高压真实气体效应主要在冷驱动气体中发生作用,其作用效果主要是使当地声速增大,从而使得入射稀疏波和反射稀疏波的传播速度加快;另一方面,高压气体效应在高温气体效应较显著的被驱动气体中作用微弱,且对激波管产生激波的强度和激波后的流动状态影响甚微。稀疏波的加快传播改变了激波管波系的相干时空关系。提前抵达的稀疏波可在一定情况下侵蚀激波风洞的有效试验时间。对于所测试的激波风洞构型,在150 MPa氢气驱动110 k Pa氮气的工况下,高压效应导致的有效试验时间缩短约38%。适当加长驱动段长度和采用高温气体驱动均可有效减弱高压真实气体效应的影响。     

《准晶弹性的数学理论及应用》评介

20世纪80年代中期准晶的发现,曾引起晶体学、物理学、化学和材料科学界的轰动.报导其发现的论文,后来被美国<物理评论快报>(Phys.Rev .Lett.)列为该杂志发表的论文中被引用最多的前10名中的第8名(到2002年,已被引用3000多次).从那时起,准晶因具有重量轻、强度高和性能稳定的特性,所以可将其制成功能...     

New Explicit Expression of Barnett-Lothe Tensors for Anisotropic Linear Elastic Materials

The three Barnett-Lothe tensors H, L, S appear often in the Stroth formalism of two-dimensional deformations of anisotropic elastic materials [1–3]. They also appear in certain three-dimensional problems [4, 5]. The algebraic representation of H, L, S requires computation of the eigenvalues p^v(v=1,2,3) and the normalized eigenvectors (a, b). The integral representation of H, L, S circumvents the need for computing p ^v(v=1,2,3) and (a, b), but it is not simple to integrate the integrals except for special materials. Ting and Lee [6] have recently obtained an explicit expression of H for general anisotropic materials. We present here the remaining tensors L, S using the algebraic representation. They key to our success is the obtaining of the normalization factor for (a, b) in a simple form. The derivation of L and S then makes use of (a, b) but the final result does not require computation of (a, b), which makes the result attractive to numerical computation. Even though the tensor H given in [6] is in terms of the elastic stiffnesses C^μ v while the tensors L, S presented here are in terms of the reduced elastic compliances s′ _μv , the structure of L, S is similar to that of H. Following the derivation of H, we also present alternate expressions of L, S that remain valid for the degenerate cases p ₁ p ₂ and p₁=p₂ = p ₃. One may want to compute H, L, S using either C _μv or s′ _μv v, but not both. We show how an expression in C^μ v can be converted to an expression in s′ _μv v, and vice versa. As an application of the conversion, we present explicit expressions of the extic equation for p in C^μ v and s′ _μv v. This revised version was published online in August 2006 with corrections to the Cover Date.     

多圆形刚性夹杂的反平面问题

构造任意分布且相互影响的多个圆形刚性夹杂模型的复应力函数，采用复变函数方法，达到满足各个夹杂的边界条件，利用坐标变换和围线积分将求解方程组化为线性代数方程组，推导出了圆形刚性夹杂任意分布的界面应力解析表达式，算例对多夹杂与单夹杂两种模型的界面应力最大值进行了对比，同时还给出了界面应力最大值随夹杂间距的变化规律，求出了刚性夹杂的合理间距。本文发展的分析方法为研究夹杂材料的细观机理探索了一条有效的分析途径。     

圆形刚性夹杂双周期分布的反平面问题

研究含双周期分布的圆形刚性夹杂在无穷远受纵向剪切的弹性平面问题，遵循复合材料中各夹杂相互影响的重要条件。采用复变函数方法。构造相应模型的复应力函数。通过坐标变换，同时满足夹杂边界位移条件，再利用围线积分将求争方程组化为线性代数方程组。导出了圆形刚性夹杂双周期分布的界面应力解析表达式。算例给出了界面应力最大值与夹杂间距的变化规律。求出了刚性夹杂的合理间距问题，本文发展的分析方法为研究夹杂材料的细观机理探索了一条有效的分析途径。     

A material model for cementitious composite materials with an exterior point Eshelby microcrack initiation criterion

A micromechanical model for cementitious composite materials is described in which microcrack initiation, in the interfacial transition zone between aggregate particles and cement matrix, is governed by an exterior-point Eshelby solution. The model assumes a two-phase elastic composite, derived from an Eshelby solution and the Mori–Tanaka homogenization method, to which circular microcracks are added. A multi-component rough crack contact model is employed to simulate normal and shear behaviour of rough microcrack surfaces. The development of the microcrack initiation criterion and the rules adopted for microcrack evolution are a particular focus of the paper. Finally, it is shown, on the basis of several numerical simulations, that the model captures key characteristics of the behaviour of cementitious composites such as concrete.     

A Model for Predicting Effective Properties of Piezocomposites with Non-piezoelectric Inclusions

Most piezocomposites, which have been widely used in engineering, consist of piezoelectric inclusions and a non-piezoelectric matrix. Due to the limits of fabrication technology, it is hard to avoid the matrix intermingling with other non-piezoelectric inclusions, such as cavities. The non-piezoelectric inclusions can substantially affect performance of piezocomposites. In this paper we study the electromechanical fields in piezocomposites which are composed of a non-piezoelectric matrix embedded with both piezoelectric and non-piezoelectric inclusions. Closed-form relations are obtained for the effective electroelastic moduli of a piezocomposite with both piezoelectric and non-piezoelectric inclusions. The effective properties of a 1-3 type piezocomposite with non-piezoelectric spherical inclusions are analyzed carefully and explicit formulae for the effective electroelastic properties of a 1-3-0 piezocomposite are also obtained. The analysis shows that the effect of non-piezoelectric inclusions on the electroelastic properties of piezocomposites is significant and should not be neglected. The model proposed in this paper is expected to be useful for predicting and analyzing the overall electromechanical properties of piezocomposites with a non-piezoelectric matrix containing both piezoelectric and non-piezoelectric inclusions.     

Fixed-Point Theory for Weakly Sequentially Upper-Semicontinuous Maps with Applications to Differential Inclusions

We present new fixed-point theorems for weakly sequentially upper-semicontinuous maps. These results are then used to establish existence principles for second-order differential equations and inclusions.     

Modelling of Thin Elastic Plates with Small Piezoelectric Inclusions and Distributed Electronic Circuits. Models for Inclusions that Are Small with Respect to the Thickness of the Plate

This paper is devoted to the modelling of thin elastic plates with small, periodically distributed, piezoelectric inclusions, in view of active controlled structure design. The initial equations are those of linear elasticity coupled with the electrostatic equation. Different kinds of boundary conditions on the upper faces of inclusions are considered, corresponding to different ways of control: Dirichlet, Neumann, local or nonlocal mixed conditions. We compute effective models when the thickness a of the plate, the characteristic dimension ε of the inclusions, and ε / a tend together to zero. Other situations will be considered in two forthcoming papers. This revised version was published online in August 2006 with corrections to the Cover Date.