ELECTROELASTIC FIELD FOR AN IMPERMEABLE ANTI-PLANE SHEAR CRACK IN A PIEZOELECTRIC CERAMICS PLATE

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三维运动接触问题的广义Галин定理

本文给出了求解一类相当普遍的三维运动接触问题的分析解法,并且把仅仅对静态接触问题成立的 定理推广到动力学情形,作了严格证明。作为例子,对接触区为椭圆的情形给出了积分形式的解,并且作了数值计算,由这些结果可以看出运动压体速度的效应。     

The relation between the generalised Eshelby integral and the generalised BCS and DB modelsvspace1mm

The generalised BCS dislocation group model and the generalised DB atomic cohesive force zone model have obtained the same results on nonlinear fracture study of some one-, two- and three-dimensional quasicrystals. This work reveals some inherent connection between the two models, and finds that their common basis is the generalised Eshelby integral based on the generalised Eshelby energy--momentum tensor for quasicrystals. Further applications of the theory in solving nonlinear fracture problems of the materials are also discussed.     

Dynamic behaviour of the icosahedral Al--Pd--Mn quasicrystal with a Griffith crack

The dynamic response of an icosahedral Al-Pd-Mn quasicrystal with a Griffith crack to impact loading is investigated in this paper. The elastohydrodynamic model for the wave propagation and diffusion together with their interaction is adopted. Numerical results of stress, displacement and dynamic stress intensity factors are obtained by using the finite difference method. The effects of wave propagation, diffusion and phonon-phason coupling on the quasicrystal in the dynamic process are discussed in detail, where the phason dynamics is explored particularly.     

准晶数学弹性理论和某些有关研究的进展(下)

本文对固体准晶力学性能和准晶数学弹性, 塑性, 断裂以及有关研究的进展作了评论, 尤其对材料常数和塑性变形行为的测量, 一维、二维、三维准晶弹性理论, 动力学、非线性、缺陷理论、准晶弹性新型偏微分方程的推导和精确分析解, 复分析方法, 变分原理和有限元方法, 有限差分方法这些宏观问题和它们的数学方法进行了分析, 同时对准晶晶格动力学问题的数学理论也作了初步讨论. 近来在软物质中发现了12 次和18次对称准晶, 意义重大, 这里也做了初步介绍. 文中重点讨论此领域最近这些年来中国科学工作者的工作.     

On the interaction between dislocations and cracks in one-dimensional hexagonal quasi-crystals

The solution of elasticity problems involving the interaction between dislocations and cracks plays a fundamental role in many practical and theoretical applications. Although elasticity problems involving dislocation or cracks in quasi-crystals have been investigated in many papers, the analysis is limited to a single defect. This paper investigates the interaction of defects in one-dimensional hexagonal quasi-crystals using the complex variable function method. The interaction force between two parallel dislocations is presented and the analytic solutions of elastic fields of interaction between a dislocation and a crack are obtained. A version of the well-known Peach－Koehler formula in one-dimensional hexagonal quasi-crystals is given.     

一类二维对偶积分方程的解及其应用

二维对偶积分方程的理论与方法,在数学上尚未建立,因而完全的分析解不可能得到,从而使一些力学、物理与工程问题无法求解.利用双重展开和边界配置方法,得到了在数学和物理学上有着广泛应用的一类二维对偶积分方程的解答.把二维对偶积分方程化简成无限代数方程组,此方法的精确度取决于计算点的配置(即所谓边界配置).通过对固体力学中某些复杂的初值_边值问题的应用说明此是方法有效的.     

Elastic analysis of a mode II crack in a decagonal quasi—crystal

The elastic analysis of a mode II Griffith crack penetrating through a decagonal quasi-crystal along the periodic axis is made within the context of the continuum theory.By using a general solution obtained previously,tne problem in the case of uniform shear stress at infinity is solved,and the analytical expressions for the entire stress field disturbed by an internal crack are derived in an explicit form.The asymptotic fields of the displacement and stress around a crack tip in both phonon and phason fields indicate that the stresses near a crack tip exhibit the square-root singularity.The formula for evaluating the energy release rate is also given.If imposing that the phason field is absent,the well-known results of a mode II crack in a conventional material are recovered from the present results.     

PLANE ELASTICITY PROBLEM OF TWO-DIMENSIONAL OCTAGONAL QUASICRYSTALS AND CRACK PROBLEM

The plane elasticity theory of two-dimensional octagonal quasicrystals is developed in this paper. The plane elasticity problem of quasicrystals is reduced to a single higher-order partial differential equation by introducing a displacement function. As an example, the exact analytic solution of a Mode I Griffith crack in the material is obtained by using the Fourier transform and dual integral equations theory, then the displacement and stress fields, stress intensity factor and strain energy release rate can be calculated. The physical significance of the results relative to the phason and the difference between the mechanical behaviours of the crack problem in crystals and quasicrystals are figured out. These provide important information for studying the deformation and fracture of the new solid phase.     

狭长体中静态裂纹与快速传播裂纹的精确分析解

本文用保角映射把狭长形裂纹静力学第一边值问题予以统一的彻底的解决,接着对更为困难的狭长体裂纹动力学进行了研究。基于作者已有的理论框架,采用z₁平面与z₂平面同时映射到ζ平面上单位圆内部一个保角变换,使这一复杂的边值问题也得以彻底解决。在以上两种情形都得到了封闭形式的精确分析解,并且当裂纹速度V→0时,动力学解还原为静力学解。这些解在科学(例如地球物理学、地震学)和工程(例如液压断裂采油工程、爆破工程)中有一定的应用价值。