结合材料界面端的三维应力奇异性

本文利用特殊有限元方法，开发了一个用来求解结合材料界面端三维应力奇异性问题的数值分析程序。该方法只需对界面端的角度方向进行离散即可求得应力奇异性。结合材料的应力奇异性取决于两种材料的材料常数和界面端形状。选用三个材料参数作为变量，用来研究结合材料三维应力奇异性随材料常数的变化规律。文中计算了几种重要而且常见的情况，并以此为基础建立了数据库。同时，还分析了应力奇异性随界面端形状的变化规律，并得到了应力函数的分布图。     

三维双材料结构的应力奇异性分析

应用有限单元法子模型技术,对具有不同界面角的三维双材料结构的应力奇异性进行了分析。结果表明,应用子模型技术估算三维双材料结构的应力奇异性指数是有效的。然后分析了界面端线和界面端点处附近奇异性指数,得到了一些重要而有趣的结果。最后对消除三维双材料结构应力奇异性的几何条件进行了讨论。     

影响双材料界面端三维应力奇异性的几何因素研究

应用常规有限单元分析技术,对几种典型接头形式的三维双材料结构界面端点附近应力奇异性进行了研究,重点分析了棱角(两自由平面的夹角)大小对界面端点附近应力奇异性指数的影响。数值分析结果表明:棱角大小对界面端应力奇异性指数有明显影响,棱角越大,奇异性指数越小;当棱角趋于180°时,端点附近的应力奇异性指数收敛于界面端线上的值(等于平面应变条件下的理论值)。研究发现,如果采用圆弧对三维双材料结构的棱边进行倒角,使相应的界面端线变成光滑连续曲线,则原界面端点附近的应力奇异性会完全退化为界面端线附近的应力奇异性,即界面端点独特的应力奇异性现象消失。     

电致伸缩材料内电极附近应力奇异性研究

应用复变函数的方法,研究电致伸缩材料内置电极附近的应力奇异性.基于精确的电边界条件,采用Hilbert理论以及复变函数中的Cauchy积分与留数定理,首先分别给出了柔性电极和刚性电极的复势函数解,然后就这两种极限情况,讨论了电极刚度对应力场奇异性的影响.研究结果表明:无论对柔性电极还是刚性电极,Max-well应力的应力场均呈现r-1阶的奇异性,但对于前者总应力奇异性系数为零,而对于后者总应力奇异性系数与基体的材料常数有关.     

纤维与基体的轴对称界面端附近的奇异应力场

基于各向性弹性力学空间轴对称问题的基本方程,研究了纤维与基体的轴对称界面端的应力奇异性,并给出了界最佳 近的奇异应力场。研究结果表明,该轴对称界面端的应力奇异性与平面应变状态下相应模型的应力奇异性完全相同,材料对界面端附近奇异应力场的影响可用丰个双材料组合参数描述。     

轴对称界面端的扭转问题

基于弹性力学轴对称扭转问题的通解,研究了具有任意几何形状的双材料轴对称界面端,给出了界面端的应力奇异性及其附近的位移场和奇应力场,定义了扭转问题的Ｄｕｎｄｕｒｓ双材料参数。研究结果表明,应力奇异性只与界面端的结合角和扭转问题的Ｄｕｎｄｕｒｓ双材料参数有关,而与界面的角度以及界面端与对称轴之间的距离无关,在任何情况下,特征值均为实数,不会产生振荡应力奇异性。     

各向同性材料接头和界面相交裂纹应力奇异性特征分析

提出了用插值矩阵法分析各向同性材料接头以及与界面相交的平面裂纹应力奇异性。基于接头和裂纹端部附近区域位移场渐近展开,将位移场的渐近展开式的典型项代入线弹性力学基本方程,得到关于平面内各向同性材料接头以及与两相材料界面相交裂纹应力奇异性指数的一组非线性常微分方程的特征值问题,运用插值矩阵法求解,获得了两相材料平面接头端部应力奇异性指数以及与界面以任意角相交的裂纹尖端的应力奇异性指数随裂纹角的变化规律,数值计算结果与已有结果比较表明,本文方法具有很高的精度和效率。     

异质材料粘接界面强度——三维应力奇异性影响

通过实验并结合有限元分析研究了三维应力奇异性对异质材料粘接接头界面强度的影响.有限元分析结果表明:如果对三维双材料结构的棱边进行圆弧倒角,使相应的界面端线变成光滑连续曲线,则原界面端点附近的三维应力奇异性会退化为界面端线附近的二维应力奇异性,进而降低应力奇异性程度.设计了一系列有圆弧倒角与无圆弧倒角的聚甲基丙烯酸甲酯(PMMA)/铝(AL)和聚碳酸酯(PC)/铝(AL)双材料试样并进行了四点弯曲实验.实验结果表明:界面尺寸对试样失效载荷无明显影响;与未圆弧倒角的试样相比,有圆弧倒角试样的失效载荷明显得到提高.这一结果证明三维应力奇异性对粘接界面强度有明显影响.     

考虑尺寸效应的双材料轴对称界面端应力奇异性

提出了一种分析双材料轴对称界面端的应力奇异行为的特征值法.基于弹性力学空间轴对称问题的基本方程和一阶近似假设,利用分离变量形式的位移函数和无网格算法,导出了关于应力奇异性指数的离散形式的奇异性特征方程.由奇异性特征方程的特征值和特征向量,即可确定应力奇异性指数、位移角函数和应力角函数.数值求解了纤维/基体轴对称界面端模型的奇异性特征方程, 结果表明:尺寸效应参数δ(奇异点与轴对称轴的距离和应力奇异性支配区域大小的比值)影响着应力奇异性的强弱与阶次, 准一阶近似解析解只是δ>>1时的一个特例.      

各向同性与各向异性三相材料接头应力奇异性研究

研究了各向同性与各向异性三相材料接头的应力奇性指数,通过引入奇异点附近区域位移场渐近展开的典型项,将各向同性与各向异性组合材料接头的控制方程和径向边界条件转化为变系数常微分方程的特征值问题;再利用插值矩阵法求解所建立的特征方程,得到接头端部的应力奇性指数和特征角函数。对由两个各向异性材料和一个各向同性材料以任意楔形角组成的三相接头结构的奇异性进行了研究,并比较了它们的应力奇性指数。计算结果表明:对于粘结接头,各向同性材料刚度越大应力奇异性越强;对于剥离接头,各向同性材料楔形角或材料刚度越大,第一阶应力奇异性越弱。计算结果与已有文献的结果对比吻合良好,证明了本文方法的有效性。     

固体跨尺度压痕标度律的研究与展望

压痕标度律是对通过压痕试验方法测定固体材料力学性能参量问题所给出的一般性结论, 具有重要的理论意义, 是探寻材料力学性能潜在规律的方法论研究. 本综述论文系统而简要地介绍如下主要内容: 采用传统理论对传统固体材料压痕标度律的研究回顾; 采用跨尺度力学理论对先进固体材料的跨尺度压痕标度律的研究回顾. 总结并得到了如下主要结论: 传统固体材料压痕标度律可由一空间曲面完整描绘, 若进一步已知某类无量纲独立参量的取值范围, 则该空间曲面可退化为系列平面曲线族; 先进固体材料(新材料)的跨尺度压痕标度律可由一个三维函数关系完整描绘, 若存在某类独立无量纲参量取值范围已知, 则该三维函数关系将退化为系列空间曲面族. 压痕标度律的未来研究发展仍将重点集中在建立新材料的跨尺度压痕标度律上, 以试图从根本上解决新材料力学性能标准规范难以建立的理论问题. 除此之外也将重点关注建立各类功能新材料的多尺度及跨尺度压痕标度律规律.      

Some exact solutions for a class of compressible non-linearly elastic materials

In this paper we consider exact solutions for plane and axisymmetric deformations for a class of compressible elastic materials we call coharmonic. The coharmonic materials are derived from the harmonic materials by using Shield's inverse deformation theorem. The governing equations for the coharmonic material show the same kind of simplification associated with the harmonic materials. The equations reduce to first-order linear equations depending on an arbitrary harmonic function. They are intractable in general, so various ansätze are investigated. Boundary value problems for the coharmonic materials are compared with the same problems for harmonic materials. For certain boundary value problems, the harmonic materials exhibit well-known problematic behaviour which limits their use as models of material behaviour. The corresponding solutions for the coharmonic materials do not display these non-physical features.     

侵彻条件下两类靶体材料静阻力的探讨

以空腔膨胀理论为主要理论工具,通过比较侵彻近区塑性材料和脆性材料动力学行为的差异,对两类不同材料静阻力（R_t）的本质进行探讨,并对脆性材料侵彻的若干应用问题提出建议。研究表明：（1）R_t是靶体介质以固体特性抵抗局部扩孔、具有时间平均特性的弹体横截面平均应力,其具体取值随着材料的物理力学特性、侵彻模型、撞击速度等因素而变化,因此不是材料的固有特性。（2）对于塑性靶体的非变形侵彻问题,静态空腔膨胀理论的结果能够对R_t作出比较合理的预测;对于拟流体侵彻问题,一般需要对静态空腔膨胀理论的结果加以修正。（3）脆性材料的R_t主要取决于破碎后介质的力学特性而与完整材料的力学特性关系不大,且与单轴抗压强度之间不满足纯粹的单调关系;当侵彻速度较低时,应考虑侵彻速度对侵彻阻力的强化作用,这种强化作用的本质是内摩擦;当侵彻速度足够高时,脆性材料体现出恒定不变的“动力硬度”,其反映了材料的本征阻力特性。（4）提高脆性材料的侵彻阻力的关键在于减小应力波峰值后环向拉应力的幅值、抑制材料的破碎速度和程度,具体措施包括主动或被动地增加外围压、对基质中添加增韧增强纤维等;为了实现对脆性材料侵彻问题更高精度的数值模拟,建议更加重视对破碎介质动力学特性的研究。

     

Green's function solution and displacement potentials for Transformed Transversely Isotropic materials

A totally non-degenerate expression for the Green's function of infinite Transversely Isotropic (TI) materials is first deduced from the solutions given by Pan and Chou [Pan, Y.-C., Chou, T.-W., 1976. Point force solution for an infinite transversely isotropic solid. Trans. ASME, J. Appl. Mech. 43 (4), 608–612]. Then this solution and also the displacement potentials for TI materials are extended by a linear transformation to a larger family of anisotropic materials (Transformed Transversely Isotropic or TraTI materials). This family depends on 12 independent parameters and contains non-orthotropic materials and in this way a first explicit analytical solution for the Green's function for a non-orthotropic material is obtained. The TraTI materials which have orthotropic Symmetry (StraTI materials) constitute a sub-family depending on 6 independent parameters in the symmetry basis of the material. These materials present a 3D anisotropy (different stiffnesses in three orthogonal directions). General displacement potentials and the Green's function solution for STraTI materials can be deduced by a simple change and introducing one additional parameter in the well-known TI solutions.     

基于金相图片识别功能梯度材料参数的梯度分布函数

功能梯度材料具有复杂的细观结构.其内部构造远比匀质材料复杂.以目前的实验条件,测量功能梯度材料参数分布函数一般是十分困难的.该文提出一种细观元方法,直接利用功能梯度材料金相图片信息,来进行功能梯度构件宏观响应的跨尺度力学分析.另在功能梯度材料结构静、动力正演分析基础上,根据正演所求得的挠度或固有频率值,采用混和罚函数法来反演识别功能梯度材料参数的宏观梯度分布函数.     

多尺度复合材料力学研究进展

多尺度复合材料力学是运用多尺度分析思想研究空间分布非均匀材料力学性能的学科.近年来,多组分、多层级先进材料的蓬勃发展和微纳米实验观测手段的不断进步,有力地推动了该学科的研究.论文围绕非均匀材料力学性能的多尺度分析,首先从微纳米尺度到宏观尺度综述了常用的理论分析方法;接着分别针对非均匀连续介质和离散体系介绍了常用的多尺度计算模拟方法;然后结合本课题组在纳米复合材料、抗冲击吸能材料、随机网络材料和多层级自相似材料等方面的研究工作,举例说明了如何综合运用多种方法对各种复杂材料系统进行多尺度分析;最后,展望了该领域还需进一步发展和完善的若干方向.     

Plane-strain crack-tip stress field for anisotropic perfectly-plastic materials

Plane-strain crack-tip stress solutions for anisotropic perfectly-plastic materials are presented. These solutions are obtained using the plane-strain slip-line theory developed by Rice (1973). The plastic anisosotropy is described by the Hill quadratic yield condition. The crack-tip stress solutions under symmetric (Mode I) and anti-symmetric (Mode II) conditions agree well with the low-hardening solutions for the corresponding power-law hardening materials. The crack-tip stress solutions under mixed Mode I and II conditions are also presented. All the solutions indicate that the general features of the slip-line field near a crack tip in orthotropic plastic materials with the elliptical yield contours in the Mohr plane are the same as those associated with isotropic plastic materials. However, the angular variations of the crack-tip stress fields for the materials with large plastic orthotropy differ substantially from those for isotropic plastic materials. Modifications due to polygonal yield contours are outlined and implications of solutions to the fracture analysis of ductile composite materials containing macroscopic flaws are discussed.     

The role of mechanics in biological and biologically inspired materials

In the development of new materials, researchers have recently turned to nature for inspiration and assistance. A special emphasis has been placed on understanding the development of biological materials from the traditional correlation of structure to property, as well as correlating structure to functionality. The natural evolution of structure in biological materials is guided by the interaction between these materials and their environment. What is most notable about natural materials is the way in which the structure is able to adapt at a wide range of length scales. Much of the interaction that biological materials experience occurs through mechanical contact. Therefore, to develop biologically inspired materials it is necessary to quantify the mechanical behavior of and mechanical influences on biological structures with the intention of defining the natural structure-property-functionality relationship for these materials. In particular, the role mechanics has assumed in understanding biological materials, and the biologically inspired materials developed from this knowledge, will be clarified. The following will serve to elucidate on this role: the helical structure of fibrous tissue, the multi-scale structure of wood, and the biologically inspired optimal structure of functionally graded materials.     

Plane strain extension of a strip made of a material with stress state type dependent properties and weakened by cuts with circular base

The limit properties of many heterogeneous materials such as grounds, concrete, ceramics, cast-iron alloys, and various heat-resistant and powder materials, as well as the properties of many composite materials, depend on the loading conditions. Neglecting the effects exhibited by such materials may result in nonconservative limit load analysis for some types of loading and possibly in an overly increased end product weight by failing to take into account stronger material properties for other types of loading. This paper presents a possible approach to modeling the behavior of such materials under plastic deformation, which is demonstrated for the sample problem on the extension of a strip weakened by cuts with circular base. An analytic solution on the basis of a rigid-plastic model of the material and a numerical solution by the finite elementmethod with elastic strains and small strengthening taken into account are presented.     

Preparation and functionalization of mesoporous silica spheres as packing materials for HPLC

This paper presents the integrated results of a series of new methods for preparing mesoporous silica spheres as high-performance liquid chromatography （HPLC） packing materials. The separation performance of the mesoporous spheres materials has also been determined. Micrometer- sized silica spheres with uniform spherical morphologies and ordered mesostructures were first successfully synthesized by the method employing a water-soluble polymer-assisted assembly. Then the templates for getting ordered mesoporous materials with high-density silanol groups were removed by using hydrothermal oxidation. Finally the silica spheres were functionalized with C8 alkyl groups by surface modification under hydrothermal conditions. The resultant functionalized silica spheres were demonstrated to be excellent oacking materials for HPLC.