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。     

夹杂和裂纹的相互作用及端点相交的奇性性态分析

利用单根裂纹和单根夹杂的基本解,通过弹性力学的线性叠加原理,将平面裂纹和夹杂相互作用的问题归结为解一组带有柯西型奇异积分的积分方程组,计算了裂纹和夹杂端点的应力强度因子,给出了一些数值例子,并对夹杂和裂纹水平接触时的情形作了奇性分析,结果可作为研究夹杂尖端引起的裂纹及其扩展的工程分析的计算模型。     

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。中结果对研究新型复合材料有一定的应用价值。     

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日(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。     

刚性线夹杂与弹性圆夹杂的相互作用

本文将刚性线夹杂与弹性圆夹杂的相互作用，归为解一个标准的柯西型奇异积分方程，获得了刚性夹杂端点的应力强度因子及夹杂的界面应力．     

压应力状态下细观非均匀性岩石的损伤局部化和应力应变关系分析

利用摩擦弯折裂纹模型研究了受压条件下细观非均匀性岩石的损伤局部化问题和全过程应力应变关系．模型考虑了裂纹相互作用对损伤局部化和全过程应力应变关系的影响，确定了损伤局部化发生的条件，分析了产生损伤局部化的原因．研究表明全过程应力应变关系包括线弹性阶段、非线性强化阶段、应力降和应变软化阶段．通过和实验对比分析验证了模型的正确性和有效性．     

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.     

平面应力裂纹问题的高阶渐近场

本文对平面应力I型裂纹问题高阶渐近场,进行了严格的数学分析.证实了二阶渐近场不是含有独立常数的高阶本征场,而必须与一阶渐近场的弹性应变项相匹配.二阶渐近场对裂纹前方的应力场的影响很小.裂纹前方应力场由HRR奇性场表征,因而J积分单参数准则可以作为平面应力问题的起裂准则.     

On the solution of boundary value problems on an inhomogeneous plane with a crack and a barrier connected in series

We consider boundary value problems for an equation in divergence form on a plane divided into two inhomogeneous half-planes by a film inclusion in the form of a strongly permeable crack and a weakly permeable barrier connected in series; this models a contact of heterogeneous media under inhomogeneous external conditions. The desired potentials have prescribed singular points (sources, drains, etc.). The coefficients of the equation are nonconstant and may increase or decrease when moving away from the film inclusion along a family of parabolas. We obtain representations of solutions of the considered problems via harmonic functions with the corresponding singular points on the plane.     

含圆形孔口和水平直裂纹的平面问题的应力分析

利用复变函数方法和积分方程理论研究了既含有圆形孔口又含有水平裂纹的无限大平面的平面弹性问题,将复杂的解析函数的边值问题化成了求解只在裂纹上的奇异积分方程的问题.此外,还给出了裂纹尖端附近的应力场和应力强度因子的公式.     

A CRACK PROBLEM WITH A BROKEN LINE INTERFACE

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The contact problem of elasticity theory for bodies with cracks

The plane contact problem of a stamp impressed into an elastic half-plane containing arbitrarily arranged rectilinear subsurface cracks is formulated and investigated by asymptotic methods. Partial or total overlapping of the crack edges is assumed. The problem reduces to a system of linear singular integrodifferential equations with side conditions in the form of equalities and inequalities. An analytic solution of the problem is obtained in the form of asymptotic power series /1/ in the relative dimension of the greatest crack. Dependences of the first terms of the asymptotic expansions of the desired functions on the mutual location of the cracks and the contact domains, the pressure and friction stress distributions, and the crack size and orientation are determined. Numerical results are presented.

Analysis of the influence of the stress-free boundary of the half-plane on the state of stress and strain of the elastic material near the cracks is presented in /2, 3/. The problem of a crack in an elastic plane whose edges overlap partially is also examined in /3/ by numerical methods.     

The contact problem for a piecewise-homogeneous plane with a finite inclusion

A piecewise-homogeneous elastic orthotropic plate, reinforced with a finite inclusion, which meets the interface at a right angle and is loaded with shear forces, is considered. The contact stresses along the contact line are determined, and the behaviour of the contact stresses in the neighbourhood of singular points is established. By using the methods of the theory of analytic functions, the problem is reduced to a singular integro-differential equation in a finite section. Using an integral transformation, a Riemann problem is obtained, the solution of which is presented in explicit form.     

In-plane loading of a cracked elastic solid by a disc inclusion with a Mindlin-type constraint

The paper examines the problem related to the axisymmetric interaction between an external circular crack and a centrally placed penny-shaped rigid inclusion located in the plane of the crack. The interface between the inclusion and the elastic medium exhibits a Mindlin-type imperfect bi-lateral contact. Analytical results presented in the paper illustrate the manner in which the lateral translational stiffness of the inclusion and the stress intensity factor at the boundary of the external circular crack are influenced by the inclusion/crack radii ratio.