断裂动力学的进展

引言断裂动力学是断裂力学的一个新的分支,它的最早经典性文献是英国著名物理学家N.F.Mott 1948年的论文。但它真正成为一门科学,是最近10多年的事。它的一些最重要的基本概念只是在最近10多年才逐渐建立起米,比较系统的分析方法也是最近形成的,比较有效的实验研究方法建立得更晚,在70年代中后期才出现。这些情况表明它是一门新兴的      

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

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.     

平面十次对称准晶中Ⅱ型Briffith裂纹的求解

应用应力函数法,求解了二维十次对称准晶中的Ⅱ型Griffith裂纹问题。特别是把二维准晶的弹性力学问题分解成一个平面应变问题与一个反平面问题的叠加,通过引入应力函数,把平面应变问题的十八个弹性力学基本方程简化成一个八阶偏微分方程,并且求出了其在Ⅱ型Griffith裂纹情况的混合边值问题的解,所有的应力分量和位移分量都用初等函数表示出来,并且由此得出了准晶中Ⅱ型Griffith裂纹问题的应力强度因子和能量释放率。     

The stress field and energy of screw dislocation in smectic A liquid crystals and the mistakes of the classical solution

The mistakes in the classical solution of a screw dislocation in smectic A liquid crystals are pointed out. A serious problem with the well-known theory is pointed, which may be named de Gennes-Kleman-Pershan paradox and has existed for many decades in the scientific community of liquid crystal study. The correct solution is given in this paper by a simplest, elementary, and straight forward method. In connection with this, the stress field and energy of dislocation are discussed in detail. The present article provides the correct stress field and dislocation energy as well.     

Possible Mechanism of Plasticity Influenced by Magnetic Field

The strain energy of an edge dislocation in an external static magnetic field is determined by the theory of elasticity and electrodynamics according to the Volterra dislocation model for continuous media. The results show that the strain energy of the edge dislocation in paramagnetic states is increased due to static magnetic field and the increase in the energy of the dislocation is capable of influencing the dislocation depinning which leads to the change of plasticity. This gives an explanation on plasticity induced by magnetic field.     

弹性半平面中的斜边界裂纹问题

讨论了一群性半平面无限体中含有一斜烈纹的静力学问题,研究中以断裂力学原理为基础,采用了复变函数的方法,将原问题化为一组解析函数边值问题的求解。文中通过分析函数法以及应用Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ（Ｒ－Ｈ）边值问题的一般理论,给出了所研究问题的解析解,并且给出了此问题的应力强度因子Ｋ１,Ｋ１的显式形式,此外,裂纹上的位移发生的错动可以得以进一步的讨论,文中的结论对地学的研究有一定的应用价值。     

平面五次对称准晶中一类混合边值问题的交替解法与直接积分法

发展了平面五次对称准晶的数学弹性理论,并且针对裂纹这一类面缺陷的混合边值问题进行求解,求解中创议了交替法与直接积分法,用这2种方法都得到了分析解,所有的场变量都表示成初等函数,尤其是直接积分法得到的解是封闭解,为进一步研究准晶中与面缺陷有关的力学性能奠定了基础。     

Laplace变换的数值反演

本文根据作者使用 Laplace 变换数值反演的实际经验,对若干数值反演方法进行评论.实践经验表明,基于 Jacobi 正交多项式的数值反演方法计算精度较好,但仍然存在问题。 作者在实际工作中作了某些改进.对某些新近发表的数值反演方法,本文也作了简短评述,有关它们的数值试验,正在进行之中.     

瞬态接触动力学的三维问题

发展了三维瞬态接触动力学问题的分析解法,并且得到了广义Galin()定理.对于给定的相当普遍的接触应力,可以确定相应的接触位移,并且得到解析的形式;反过来,对于给定的相当普遍的接触位移,可以解析地确定其相应的接触应力.上述所指的普遍的给定物理量可以是X与y的任意阶多项式和时间t的任意瞬态函数.还针对不同接触区的几何特征和最典型的最常使用的7种固体介质进行了实例计算,所有计算结果均表明上述理论结果在数学上和物理上的精确性.