热电材料中含椭圆夹杂问题的精确解

主要研究了热电材料中含椭圆夹杂问题.假定受到无穷远处的热流和电流荷载条件下,采用保角变换和复变函数方法研究了热电材料中的椭圆夹杂问题,得到了基体和夹杂中的温度场和电场的复势表达式,还通过数值算例分析了椭圆夹杂物对热流和电流的影响.     

压电螺型位错和含界面裂纹圆形夹杂的电弹干涉效应

研究了在无穷远反平面剪切和面内电场共同作用下压电材料基体中一个压电螺型位错与含界面裂纹圆形弹性夹杂的电弹耦合干涉作用．运用复变函数方法，获得了该问题的一般解答。作为典型算例，求出了界面含一条裂纹时，基体和夹杂区域复势函数的封闭形式解以及裂纹尖端应力和电位移场强度因子。应用扰动技术和广义Peach-Koehler公式，导出了位错力的解析表达式。数值结果表明，界面裂纹对压电螺型位错与夹杂的干涉具有强烈扰动效应，当裂纹长度达到临界值时，可以改变其干涉机理．同时，分析说明压电材料中软夹杂可以排斥基体中的位错。     

含椭圆形夹杂的压电材料平面问题

应用复变函数的Ｆａｂｅｒ级数展开方法，本文研究了含椭圆形夹杂的压电材料平面问题，给出了问题的封闭解·解答表明，椭圆夹杂内的应力、应变、电场强度和电位移均为常量·通过算例，还讨论了正、逆压电效应在基体孔周处的机电行为·     

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。     

颗粒增强复合材料相界面的动态应力分析

针对硬微粒填充高聚物复合材料因相界面脱粘开裂生成微孔洞的微损伤成核机制,取材料的代表体积单元进行动力分析,通过对粘弹性基体本构关系作Ｌａｐｌａｃｅ变换建立了基本方程,并引入Ｈａｎｋｅｌ变换,得到了球对称动荷载作用下相界面应力变化规律的解析解,据此分析了惯性效应和粘性效应对界面脱粘的影响。     

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。正如所预测的,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。     

含椭圆夹杂二维各向异性电磁弹性介质的耦合问题

研究了无限大二维各向异性电磁弹性固体的椭圆的夹杂问题。基于广义Stroh方法、保角变换和扰动概念，得到了基体和夹杂内电场、磁场和弹性场的封闭解，本结果可用于研究电磁 弹性复合材料的有效性能。     

压电复合材料圆形夹杂中螺型位错和界面裂纹的干涉分析

研究了无穷远纵向剪切和面内电场共同作用下，压电复合材料圆形夹杂中螺型位错与界面裂纹的电弹耦合干涉作用．运用Riemann-Sehwarz对称原理，并结合复变函数奇性主部分析方法，获得了该问题的一般解答．作为典型算例，求出了界面含一条裂纹时基体和夹杂区域复势函数和电弹性场的封闭形式解．应用广义Peach-Koehler公式，导出了位错力的解析表达式．分析了裂纹几何参数和材料的电弹性常数对位错力的影响规律．结果表明，界面裂纹对位错力和位错平衡位置有很强的扰动效应，当界面裂纹长度达到临界值时，可以改变位错力的方向．该结果可以作为格林函数研究圆形夹杂内裂纹和界面裂纹的干涉效应．其公式的退化结果与已有献完全一致．     

夹杂与基体对界面层螺旋位错的干涉效应

研究圆形夹杂与基体对有限厚度界面层螺旋位错的干涉问题．结合复变函数的分区亚纯函数理论、施瓦兹对称原理与柯西型积分运算，发展了多连通域联结问题的一个有效分析方法，将3个区域应力函数的联结问题化归为界面层应力函数的函数方程，并求得了显式级数解．利用该结果，研究与讨论了界面层螺旋位错能与位错力．     

界面性能对陶瓷基复合材料桥联增韧的影响

对单向纤维增强陶瓷基复合材料内垂直于纤维的基体裂纹扩展和偏转条件进行研究,侧重于界面性能对裂纹尾区桥联力学分析的影响。结果表明:在界面相脱粘摩擦区和弹性滑移区共同影响下,界面韧性g_i与增强纤维相关联参量(σ_cr²r/E_f)比值是界面脱粘的重要控制条件,并决定主裂纹是否转向,脱粘发生后脱粘摩擦区的长度取决于摩擦力τ₀并与其成反比.此外,界面厚度、剪切模量等也对桥联断裂分析产生重要影响.     

Debonding of an elastic inhomogeneity of arbitrary shape in anti-plane shear

We investigate the anti-plane shear problem of a curvilinear crack lying along the interface of an arbitrarily shaped elastic inhomogeneity embedded in an infinite matrix subjected to uniform stresses at infinity. Complex variable and conformal mapping techniques are used to derive an analytical solution in series form. The problem is first reduced to a non-homogeneous Riemann–Hilbert problem, the solution of which can be obtained by evaluating the associated Cauchy integral. A set of linear algebraic equations is obtained from the compatibility condition imposed on the resulting analytic function defined in the inhomogeneity and its Faber series expansion. Each of the unknown coefficients in the corresponding analytic functions can then be uniquely determined by solving the linear algebraic equations, which are written concisely in matrix form. The resulting analytical solution is then used to quantify the displacement jump across the debonded section of the interface as well as the traction distribution along the bonded section of the interface. In addition, our solution allows us to obtain mode-III stress intensity factors at the two crack tips. The solution to the anti-plane problem of a partially debonded elliptical inhomogeneity containing a confocal crack is also derived using a similar method.     

Fracture of fiber-reinforced materials

The fracture behaviour of fiber-reinforced materials is studied in this paper. Using a simple shear lag model, which includes friction at the debonded interface and the Poisson contraction of the fiber, the fiber-matrix debonding problem is solved. This gives the relationship between debonding load and debonded length. Interfacial friction is shown to have a significant effect on the debonding load. The fracture toughness of fiber-reinforced materials due to fiber debonding, frictional dissipation at fibre-matrix interface following debonding and other micro-fracture mechanisms is discussed with reference to strong and weak fibres. Finally, the strength and toughness of short fibre-reinforced materials are given.On leave from Harbin Shipbuilding Engineering Institute, Harbin, China     

Line singularity inside an elliptic inhomogeneity

The problem of an elliptic insert with a point of elastic singularity and a perfectly adhering interface is solved using the complex variable method. In particular, it is found that the remote field is insensitive to the inhomogeneity shape and interface status. Unified formulae for the special cases of free elliptic disk and rigid matrix are written and discussed. A closed-form solution for an arbitrary line singularity inside a circular inhomogeneity is also derived as a special case.     

Elastic field perturbation by an elliptic inhomogeneity with a sliding interface

Summary Muskhelishvili complex potentials are used to solve the problem of an infinite elastic plane containing an elliptic inhomogeneity with a sliding interface but no eigenstrain. The boundary conditions considered are (a) continuity of normal tractions and displacements and vanishing shear tractions at the interface, and (b) vanishing stresses at infinity. After a conformal mapping of the elastic plane, the solution is obtained in terms of a set of infinite algebraic equations yielding the Laurent's expansion coefficients of the complex potentials. Distinct sets of formulae must be written for a circular inhomogeneity (degenerate ellipse) and an elliptic inhomogeneity (no degeneracy), and in both cases no closed-form solution is obtainable. For an elliptic inhomogeneity the solution requires iteration and recursion, and implies vanishing stresses in the homogeneity when the system is loaded with a remote uniform shear parallel to the axes of the ellipse.

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Riassunto I potenziali complessi di Muskhelishvili vengono usati per risolvere il problema di un piano elastico infinito contenente una disomogeneità ellittica con interfaccia scorrevole e che non sia all' origine di un campo di sforzi in terni. Si considerano le condizioni al contorno: (a) continuità delle trazioni e degli spostamenti normali e annullamento delle trazioni tangenziali all' interfaccia; (b) annullamento degli sforzi all' infinito. Mediante una trasformazione conforme del piano elastico, la soluzione viene espressa in termini di un sistema di infinite equazioni algebriche per i coefficienti degli sviluppi di Laurent dei potenziali complessi. Si trova che occorre scrivere distinti sistemi per i casi di disomogeneità circolare (ellisse degenere) e di disomogeneità ellittica (non circolare). In ambedue i casi non è ottenibile una soluzione in forma chiusa. Nel caso di disomogeneità ellittica la soluzione consiste in formule ricorrenti e richiede iterazione; inoltre, essa implica l'annullamento del campo di sforzi nella disomogeneità quando il sistema è soggetto ad uno sforzo di taglio uniforme applicato all' infinito parallelamente agli assi dell' ellisse.

     

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.     

AN EMBEDDED BOUNDARY METHOD FOR ELLIPTIC AND PARABOLIC PROBLEMS WITH INTERFACES AND APPLICATION TO MULTI-MATERIAL SYSTEMS WITH PHASE TRANSITIONS

The embedded boundary method for solving elliptic and parabolic problems in geometrically complex domains using Cartesian meshes by Johansen and Colella （1998, J. Comput. Phys. 147, 60） has been extended for elliptic and parabolic problems with interior boundaries or interfaces of discontinuities of material properties or solutions. Second order accuracy is achieved in space and time for both stationary and moving interface problems. The method is conservative for elliptic and parabolic problems with fixed interfaces. Based on this method, a front tracking algorithm for the Stefan problem has been developed. The accuracy of the method is measured through comparison with exact solution to a two-dimensional Stefan problem. The algorithm has been used for the study of melting and solidification problems.     

Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites

A model for a macroscopic crack transverse to bridging fibers is developed based upon the Coulomb friction law, instead of the hypothesis of a constant frictional shear stress usually assumed in fiber/matrix debonding and matrix cracking analyses. The Lamé formulation, together with the Coulomb friction law, is adopted to determine the elastic states of fiber/matrix stress transfer through a frictionally constrained interface in the debonded region, and a modified shear lag model is used to evaluate the elastic responses in the bonded region. By treating the debonding process as a particular problem of crack propagation along the interface, the fracture mechanics approach is adopted to formulate a debonding criterion allowing one to determine the debonding length. By using the energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber-reinforced composite is formulated in terms of friction coefficient and debonding toughness. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model is compared with those predicted by the models of constant frictional shear stress. The effect of Poisson contraction caused by the stress re distribution between the fiber and matrix on the matrix cracking mechanics is shown and discussed in the present analysis. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 171–190, March–April, 2007.     

Parallel two-level Schwarz methods for singularly perturbed elliptic problems

Schwarz domain decomposition methods are developed for the numerical solution of singularly perturbed elliptic problems. Three variants of a two-level Schwarz method with interface subproblems are investigated both theoretically and from the point of view of their computer realization on a distributed memory multiprocessor computer. Numerical experiments illustrate their parallel performance as well as their behavior with respect to the critical parameters such as the perturbation parameter, the size of the interface subdomains and the number of parallel processors. Application of one of the methods to a model problem with an interior layer of complex geometry is also discussed. This revised version was published online in June 2006 with corrections to the Cover Date.