平移断层的倾角对地震产生的影响

利用边界单元法和滑移弱化摩擦本构关系分析了平移断层上地震的产生。从依赖于速率和状态的摩擦本构关系出发,通过忽略速度的影响得到了滑移弱化摩擦本构关系。建立了两种本构关系之间的联系,使得在两种模型中可以使用共同的参数。通过将地球表面模拟成一个包含在无穷大弹性介质中的无穷大裂纹,已有的边界积分方法可以直接用来分析断层的滑移。由于断层上的摩擦本构关系的非线性,得到的方程也是非线性的,采用牛顿迭代法进行求解。通过数值计算得到了平移断层上滑移位移、速度及摩擦力的分布规律。考察了平移断层的倾角对地震产生的影响,计算结果表明断层的倾角越小,地震产生的位置离地球表面越近且地震产生所需滑移的时间越短。     

非连续变形计算力学模型的粘弹性分析方法Ⅱ:算例分析

应用作者提出的非连续变形计算力学模型粘弹性分析方法对具体的多体系统在动力外荷载作用下的响应进行了数值模拟，探讨了系统中物体的粘性阻尼对整个系统的变形、应力和接触应力等的影响。与通用软件ABAQUS的计算结果进行了比较研究，两种方法所得到的结果基本一致，但所发展的方法克服了ABAQUS中接触应力分段均匀分布的缺陷，因而所得到的接触应力较为合理，同时也说明了所提出的方法为由刚体、弹性体和粘弹性体所构成的复杂多体系统的数值分析提供了有力的工具。     

用松弛代数法解粘弹性体结构的应力

求解非均质的粘弹性体结构由支承变位与物体变形变化产生的应力问题,传统方法的基本困难在于解积分方程组,以致在实际计算中限制了它的应用。本文根据粘弹性体力学的基本定理以及松弛系数和变形模量的概念,提出一种方法,将粘弹性体中应力的求解转化为相当的弹性问题,从而使计算得到简化,而所得结果有较高的精度。     

缺陷孔对平面裂纹应力强度因子的影响

带有裂纹和缺陷孔洞的板的问题是一个多连域的边值问题，这类问题适合用边界元法所具有的高精度特性来求解．采用子域边界元法，在平面应变的条件下对存在中心裂纹的平面板受远处拉伸和剪切裁荷的作用进行了数值分析．研究了圆形孔洞对Ⅰ型和Ⅱ型应力强度因子的影响，与有限元法进行了对比，求解结果更加精确．计算了椭圆形孔对Ⅰ型应力强度因子的影响，得到了一些有意义的结果，并对移动接触弹性体作用下的带裂纹板进行了钻孔研究．     

基于辛本征值方法的受约束介电弹性体中褶皱不稳定性的分析

辛弹性力学已广泛应用于弹性学中各种边值问题的精确解、计算表面波模式以及预测多层超弹性薄膜中的表面褶皱。本文展示了辛分析框架还可应用于受约束介电弹性体中的表面褶皱。机械和电位移向量是两个基本变量来描述介电弹性体中机械变形与电场紧密耦合。褶皱的临界电压可以通过引入基本变量的对偶变量来从辛本征值问题中解决。本文采用扩展的W-W（Wittrick-Williams）算法和精确的积分方法,准确而高效地解决制定的辛本征值问题的本征值。通过将褶皱电压和波数与有无表面能的褶皱基准结果进行比较,验证了辛分析的有效性。辛分析框架简洁且适用于其他不稳定问题,如分层电介质弹性体、磁弹性不稳定性以及层压复合结构的微观和宏观不稳定性。     

含界面层圆形夹杂中螺旋位错的弹性分析

研究了复合材料含界面层圆形夹杂内部的一个螺旋位错在夹杂，界面层与基体材料中产生的弹性干涉，将复变函数的分区亚纯函数理论与柯西型积分，罗朗级数相结合，求出了各分区复势的解析关系，化为一个关于界面层复势的函数方程，用显示式表达了问题的结果，揭示了界面层参数对位错干涉能与位错力的影响规律。该解析方法较经典级数方法未知量大量减少，表达式更加简洁，结果的特殊情形包含了若干已有成果。     

移动接触下求解二维闭合裂纹的双重迭代边界元法

使用子域边界元法对受移动接触弹性体作用下的二维闭合裂纹问题进行了数值计算。由于两弹性体的接触界面和裂纹表面的接触范围的大小和接触状态事先是未知的 ,对此 ,在两个接触表面同时采用迭代的方法进行了求解。在裂纹的每个裂尖上都采用了四分之一的奇异单元以保证裂尖位移场和应力场奇异性的满足。用我们编制的二维裂纹问题程序对一些中心裂纹问题进行了计算 ,计算结果与经典断裂力学的理论值比较吻合。在无摩擦的条件下 ,对一些具有不同角度且受移动接触弹性体作用下的闭合裂纹问题进行了数值计算 ,得到了一些耦合作用下的应力强度因子的计算结果     

充液层合压电圆柱壳的自由振动

推导得到轴向极化的圆柱型正交各向异性压电弹性力学的三维状态方程，采用细分近似方法，得到了状态方程的解，并建立了圆柱壳内外表面边界量之间的传递关系，分析了内充可压缩流体的层合压电圆柱壳的自由振动问题，给出了频率方程的精确形式，并作了具体计算。     

粘弹性构件应力分析的混合法

详细讨论了光测粘弹性介质中光学及力学参数测试的理论及方法。首次提出用边界元与光粘弹性法相结合求解粘弹性体中应力分析的新方法，并推导出了相应的公式．以粘弹性简支梁为实例验证了我们提出的方法．     

位错动力学方法在辐照损伤力学中的应用

核能是人类最理想的清洁能源之一，在世界能源结构中发挥着巨大作用。核裂变或核聚变导致的辐照环境会引起材料的辐照损伤，进而显著影响材料的力学性能，造成辐照硬化、脆化、蠕变、肿胀等现象。无论是预测辐照材料的服役寿命，还是设计新型的抗辐照材料，都迫切需要建立强辐照环境下的塑性力学和损伤力学理论。分子动力学方法为理解辐照材料中的原子级相互作用机理提供了诸多有价值的信息，然而受限于时空尺度难以直接用于力学理论模型的建立。晶体塑性有限元方法可用于预测辐照材料的力学响应，但是往往需要基于已知的物理模型，并且拟合实验数据。位错动力学方法是联系纳米力学与连续介质力学的桥梁，是揭示大量微结构的累积相互作用机理，建立基于物理机制的塑性力学和损伤力学理论的强有力手段。位错动力学方法起源于上个世纪八十年代，起初主要用于研究位错间的短程和长程相互作用、计算位错运动引起的塑性变形、硬化、软化、变形局部化等。本文将展示三种耦合位错动力学和辐照损伤场的方法，并系统地综述研究者近年来使用该方法在理解辐照硬化、塑性变形局部化、晶界效应、温度效应、和发展多尺度耦合方法等方面取得的进展。     

Nucleation of partial dislocations at a crack and its implication on deformation mechanisms of nanostructured metals

Nucleation of partial dislocations at a crack is analyzed based a multiscale model that incorporates atomic information into continuum-mechanics approach. The crack and the slip plane as the extension of the crack are modeled as a surface of displacement discontinuities embedded in an elastic medium. The atomic potential between the adjacent atomic layers along the slip plane is assumed to be the generalized stacking fault energy, which is obtained based on atomic calculations. The relative displacements along the slip plane, corresponding to the configurations of partial dislocations and stacking faults, are solved through the variational boundary integral method. The energetics of partial dislocation nucleation at the crack in FCC metals Al and Cu are comparatively studied for their distinctive difference in the intrinsic stacking fault energy. Compared with nucleation of perfect dislocations in previous studies, several new features have emerged. Among them, the critical stress and activation energy for nucleation of partial dislocations are markedly lowered. Depending on the value of stacking fault energy and crack configuration, the saddle-point configurations of partial dislocations can be vastly different in terms of the nucleation sequence and the size of the stacking fault. These findings have significant implication for identifying the fundamental dislocation and grain-boundary-mediated deformation mechanisms, which may account for the limiting strength and the high strain rate sensitivity of nanostructured metals.     

关联参照模型和位错发射过程的分子动力学模拟

提出关联参照模型和随位错位置变化的柔性位移边界条件．提供了一个在固定位移边界条件下位错穿越边界的方法．应用三维分子动力学方法研究了体心立方（ＢＣＣ）金属晶体钼裂尖发射位错的力学行为．     

Analysis of dislocation nucleation from a crystal surface based on the Peierls-Nabarro dislocation model

Dislocation nucleation from a stressed crystal surface is analyzed based on the Peierls-Nabarro dislocation model. The variational boundary integral approach is used to obtain the profiles of the embryonic dislocations in various three-dimensional nucleation configurations. The stress-dependent activation energies required to activate dislocations from their stable to unstable saddle point configurations are determined. Compared to previous analyses of this type of problem based on continuum elastic dislocation theory, the present analysis eliminates the uncertain core cutoff parameter by allowing for the existence of an extended dislocation core as the embryonic dislocation evolves. Moreover, atomic information can be incorporated to reveal the dependence of the nucleation process on the profile of the atomic interlayer potential as compared to continuum elastic dislocation theory in which only elastic constants and Burgers vector are relevant. Finally, the presented methodology can also be readily used to study dislocation nucleation from the surface heterogeneities such as cracks, steps, and quantum structures of electronic devices.     

A numerical analysis of cracks emanating from a surface elliptical hole in infinite body in tension

This paper deals with such a kind of surface crack problem with an approximately same depth, which is called a liked-plane crack problem. Based on the previous investigations on internal rectangular crack and surface rectangular crack in infinite solid in tension and a hybrid displacement discontinuity method (a boundary element method) proposed recently by Yan, a numerical approach for the liked-plane crack problem in hand is presented. Numerical examples are given to illustrate the numerical approach is simple, yet accurate for calculating the SIFs of a liked-plane crack. Specifically, a pair of cracks emanating from a surface elliptical hole in infinite body in tension are investigated in detail.     

Elastoplastic cracks moving in orthotropic crystals

The stress field, crack-tip plastic zones and total plastic displacement created around an infinite row of collinear elastoplastic constant width Griffith-type strip cracks moving within an orthotropic crystal are considered using the powerful method of dislocation layers. The method is applied with the BCS modelled elastoplastic cracks moving under mode III loading at constant crack-tip velocity, according to the Yoffe model. Simultaneously the analysis provides solutions for a corresponding single crack moving similarly within a finite orthotropic plate and a finite plate containing a surface crack. Analogous results for the corresponding mode I, mode II and purely elastic cracks can be deduced.     

平面刚架弹塑性大位移分析的多刚体离散元法

本文基于多刚体－弹簧系统模型，给出了求解平面刚架结构弹塑性、大位移极限承载力分析的多刚体离散元法。文中首先推导了多刚体离散元法在总体坐标下的切线刚度阵，建立多刚体离散元法的增量平衡方程；而后推导了多刚体离散元的弹塑性弹簧系数矩阵，建立了多刚体离散元内力屈服面塑性铰法的增量求解格式，成功地进行了平面钢框架的弹塑性、大位移极限承载力分析。计算结果与其他数值方法或实验结果吻合良好，显示了多刚体离散元方法进行结构极限承载力分析这一复杂问题的优越性     

Stress distribution in a two-dimensional infinite anisotropic medium with collinear cracks

The plane problem of an anisotropic material with cracks, whose surfaces are subject to surface tractions of a general kind, is studied. The medium considered if of infinite extent and the cracks are located on a single line. The Fourier transform method is employed to derive the stress and displacement components at an arbitrary point of the medium in terms of the dislocation densities and the stress discontinuities on the crack line.These formulae for stress and displacement components involve the roots of a quartic equation whose coefficients are the material constants. The cases of different roots and pairwise coincident roots are examined separately. An orthotropic medium is an important example for the case of different roots while an isotropic medium is that for the case of pairwise coincident roots. These examples are discussed in detail.As an illustration of the use of these formulae the problem of a single crack in an infinite anisotropic medium is examined in detail.Work supported in part by a grant from Council of Scientific and Industrial Research, New Delhi, India.     

The effects of couple stresses on dislocation strain energy

The correspondence theorem which relates the solutions of displacement boundary value problems in classical and couple stress elasticity is formulated and applied to derive the solutions for edge and screw dislocations in an infinite medium. The effects of couple stresses on the dislocation strain energy is evaluated for both types of dislocations. It is shown that within a radius of influence of each dislocation in a metallic crystal with dislocation density of 10¹⁰ cm⁻², the strain energy contribution from couple stresses (excluding the core energy) is about 15% in the case of an edge dislocation, and about 11% in the case of a screw dislocation. It is then shown that couple stresses make large effect on the total work of tractions acting on the dislocation core surface.     

An effective boundary element method for analysis of crack problems in a plane elastic plate

A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.