裂纹与弹性夹杂的相互影响*

本文利用无限域上单根弹性夹杂和单根裂纹产生的位移和应力,将裂纹与弹性夹杂的相互影响问题归为解一组柯西型奇异积分方程,然后用此对夹杂分枝裂纹解答的奇性性态作了理论分析,并求得了振荡奇性界面应力场,对于不相交的夹杂裂纹问题,具体计算了端点的应力强度因子及夹杂上的界面应力,结果令人满意。     

弹性线夹杂的相互干扰

利用线夹杂的工程计算模型以及无限平面中单夹杂的基本解,分析了无限平面中两根径向弹性线夹杂的相互干扰问题.并将线夹杂和线夹杂相互作用的问题归结为解一组柯西型奇异积分的积分方程组,计算了夹杂端点的应力强度因子和夹杂界面应力.给出了一些数值例子.这里的结果对于研究短纤维复合材料有一定的参考价值.     

圆形界面刚性线夹杂的反平面问题

研究了在反平面集中力和无穷远纵向剪切作用下,不同弹性材料圆形界面上有多条刚性线夹杂的问题．运用Riemann-Schwarz解析延拓技术与复势函数奇性主部分析方法,首次获得了该问题的一般解答,求出了几种典型情况的封闭解,并给出了刚性线夹杂尖端的应力场分布A·D2结果表明,在反平面加载的情况下圆形界面刚性线夹杂尖端应力具有平方根奇异性,无奇异性应力振荡;应力场与刚性线夹杂的形状,加载方式和材料性质有关．退化结果与已有的解答完全吻合．     

圆形界面刚性线夹杂的平面问题

研究了圆弧形界面刚性线夹杂的平面弹性问题．集中力作用于夹杂或基体中的任意点,并且无穷远处受均匀载荷作用．利用复变函数方法,得到了该问题的一般解答．当只含一条界面刚性线夹杂时,获得了分区复势函数和应力场的封闭形式解答,并给出刚性线端部奇异应力场的解析表达式．结果表明,在平面荷载下界面圆弧形刚性线夹杂尖端应力场和裂纹尖端相似具有奇异应力振荡性．对无穷远加载的情况,讨论了刚性线几何条件、加载条件和材料失配对端部场的影响．     

矩形弹性夹杂与裂纹相互干扰的边界元分析

使用边界元法研究了无限弹性体中矩形弹性夹杂对曲折裂纹的影响,导出了新的复边界积分方程．通过引入与界面位移密度和面力有关的未知复函数H(t),并使用分部积分技巧,使得夹杂和基体界面处的面力连续性条件自动满足,而边界积分方程减少为2个,且只具有1/r阶奇异性．为了检验该边界元法的正确性和有效性,对典型问题进行了数值计算．所得结果表明:裂纹的应力强度因子随着夹杂弹性模量的增大而减小,软夹杂有利于裂纹的扩展,而刚性较大的夹杂对裂纹有抑制作用．     

裂纹与线夹杂垂直接触问题的奇性分析

以短纤维复合等作为工程背景,采用现有文献中单裂纹和单夹杂的基本解,对于限平项（基体）上,裂纹和线夹杂的垂直接触问题从断理解力学的角度作了研究,得到了问题的积分方程,推出了接触点的性线指数,奇性应力及以此表示的接触点附近三个区域内的应力强度因子表达式,并给出一些数值结果,可供工程实际参考。     

三角形弹性夹杂对裂纹的影响

研究了三角形弹性夹杂和裂纹之间的相互影响问题。应用Chau和Wang导出的面力边值问题的边界积分方程为基本方程,用夹杂和基体交界面上的面力和位移的连续性条件为补充方程,从而得到了一组能够解决夹杂和裂纹相互影响问题的方程,最后的方程组用一种新的边界单元法求解。计算了各种不同的夹杂和基体的材料常数以及夹杂和基体之间不同距离情况下裂纹尖端的应力强度因子。文中结果对研究新型复合材料有一定的应用价值。     

压电材料椭圆夹杂界面局部脱粘问题的分析

利用复变函数方法,研究在反平面剪切和面内电场共同作用下压电材料椭圆夹杂的界面脱粘问题．假定夹杂界面脱粘导致了界面电绝缘型裂纹的产生．通过保角变换和解析延拓,将原问题化为两个黎曼-希尔伯特问题,获得了夹杂和基体复势的级数解,进而求得应力变形场以及夹杂-基体界面脱粘的能量释放率的一般表达式．通过理想粘结的椭圆夹杂、完全脱粘的椭圆夹杂、局部脱粘的刚性导体椭圆夹杂、局部脱粘的圆形夹杂等特例的分析说明了该解的有效性和通用性．     

压电基体中部分脱开的刚性导体椭圆夹杂分析

通过利用八维Stroh公式以及共形映射、解析延拓和奇点分析技术,获得了对一压电基体中已部分脱开的刚性导体椭圆夹杂二维问题的闭合形式全场解答。也推导了一些新的恒等式和求和式,通过这些恒等式及求和式可获得沿界面应力和电位移分布以及刚性夹杂转动的实形式表示。正如所预料的,在脱开界面的端部应力及电位移显现出与在压电材料Griffith界面裂纹的研究中所发现的相似的奇异行为。最后也给出了几个算例以展示所得到解答的一般性以及各种载荷条件、几何参数和机电常数等对界面处应力及电位移分布的影响。     

一维正方准晶中裂纹和刚性线夹杂的封闭形式解（英文）

通过引入广义复变函数方法,研究含裂纹和刚性体夹杂物的反平面模型的一维正方准晶问题.对于一维正方准晶,考虑周期平面为(x_1, x_2),含有宏观裂纹或刚性线夹杂,具有准周期x_3方向的原子结构存在相位位移,本文重点研究相位位移对相关物理量的影响.利用广义复变函数方法,将这两个模型简化为Riemann-Hilbert问题,得到反平面的声子场与相位场的封闭解.同时求得声子场和相位场的应力强度因子的显式解,这在断裂力学和工程领域具有广泛的应用价值.结果表明,反平面情形下,含裂纹和刚性体夹杂物的声子和相位的应力强度因子,与声子场和相位场的耦合无关.     

On elastic bodies with thin rigid inclusions and cracks

This paper is concerned with the analysis of equilibrium problems for two‐dimensional elastic bodies with thin rigid inclusions and cracks. Inequality‐type boundary conditions are imposed at the crack faces providing a mutual non‐penetration between the crack faces. A rigid inclusion may have a delamination, thus forming a crack with non‐penetration between the opposite faces. We analyze variational and differential problem formulations. Different geometrical situations are considered, in particular, a crack may be parallel to the inclusion as well as the crack may cross the inclusion, and also a deviation of the crack from the rigid inclusion is considered. We obtain a formula for the derivative of the energy functional with respect to the crack length for considering this derivative as a cost functional. An optimal control problem is analyzed to control the crack growth. Copyright © 2010 John Wiley & Sons, Ltd.     

两压电介质之间的界面夹杂问题

应用Stroh理论,研究了两压电介质之间的刚性介电线夹杂问题。首先该问题被化为Hilbert问题,然后分别给出了压电介质内的复势函数解、夹杂内的电场解和夹杂尖端场的解析表达式。结果表明,在夹杂尖端附近,所有的场变量均呈现奇异性和振荡性,且其强度取决于介质的材料常数和无限场远处的应变。此外,结果还表明,当从夹杂内部趋近夹杂尖端时,夹杂内的电场也呈现奇异性和振荡性。     

Junction problem for elastic and rigid inclusions in elastic bodies

An equilibrium problem for an elastic body is considered. It is assumed that the body has a thin elastic inclusion and a thin rigid inclusion. We analyze a junction problem assuming that the inclusions have a joint point. Different equivalent problem formulations are discussed, and existence of solutions is proved. A set of junction conditions is found. We investigate a convergence to infinity and to zero of a rigidity parameter of the elastic inclusion. A delamination of the elastic inclusion is also investigated. In this case, inequality‐type boundary conditions are imposed at the crack faces to prevent a mutual penetration between crack faces. Copyright © 2015 John Wiley & Sons, Ltd.     

On a partially debonded rigid line inclusion penetrating a circular inhomogeneity

We derive closed-form solutions to the mixed boundary value problem of a partially debonded rigid line inclusion penetrating a circular elastic inhomogeneity under antiplane shear deformation. The two tips of the rigid line inclusion are just mutual mirror images with respect to the inhomogeneity/matrix interface, and the upper part of the rigid line inclusion is debonded from the surrounding materials. By using conformal mapping and the method of image, closed-form solutions are derived for three loading cases: (i) the matrix is subjected to remote uniform stresses; (ii) the matrix is subjected to a line force and a screw dislocation; and (iii) the inhomogeneity is subjected to a line force and a screw dislocation. In the mapped ξ-plane, the solutions for all the three loading cases are interpreted in terms of image singularities. For the remote loading case, explicit full-field expressions of all the field variables such as displacement, stress function and stresses are obtained. Also derived is the near tip asymptotic elastic field governed by two generalized stress intensity factors. The generalized stress intensity factors for all the three loading cases are derived.     

A rigid inclusion in the contact problem for elastic plates

A family of problems under consideration describes the contact of elastic plates situated at a given angle to each other and, in the natural condition, touching along a line. The plates are subjected only to bending. The limiting process from the elastic inclusion to the rigid one is studied. It is demonstrated that the limit problems precisely describe the contact of an elastic plate with a rigid beam and the problem of the equilibrium of an elastic plate with a rigid inclusion. The solvability of the problems is established; the boundary conditions holding on the possible contact set are found as well as their precise interpretation.