SCATTERING OF HARMONIC ANTI-PLANE SHEAR STRESS WAVES BY A CRACK IN FUNCTIONALLY GRADED PIEZOELECTRIC/PIEZOMAGNETIC MATERIALS

In this paper, the dynamic behavior of a permeable crack in functionally graded piezoelectric/piezomagnetic materials is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with the coordinate parallel to the crack. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations in which the unknown is the jump of displacements across the crack surfaces. These equations are solved to obtain the relations between the electric filed, the magnetic flux field and the dynamic stress field near the crack tips using the Schmidt method. Numerical examples are provided to show the effect of the functionally graded parameter and the circular frequency of the incident waves upon the stress, the electric displacement and the magnetic flux intensity factors of the crack.     

SCATTERING OF THE HARMONIC STRESS WAVE BY CRACKS IN FUNCTIONALLY GRADED PIEZOELECTRIC MATERIALS

The present paper considers the scattering of the time harmonic stress wave by a single crack and two collinear cracks in functionally graded piezoelectric material （FGPM）. It is assumed that the properties of the FGPM vary continuously as an exponential function. By using the Fourier transform and defining the jumps of displacements and electric potential components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement and electric potential components across the crack surface are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the influences of material properties on the dynamic stress and the electric displacement intensity factors.     

多个纵向环形界面裂纹对P波散射的动应力强度因子

研究多个纵向环形界面裂纹的P波散射问题.以裂纹面的位错密度函数为未知量,利用Fourier积分变换,将问题归结为第二类奇异积分方程,然后通过数值求解,获得裂纹尖端的动应力强度因子.最后给出了双裂纹动应力强度因子随入射波频率变化的关系曲线.     

用子域边界元法研究各向异性材料中的界面裂纹

用子域边界元法研究各向异性材料中的界面裂纹，在边界元公式中，采用了带特征根的基本解，以增量形式的边界积分方程为基础，通过二次等参元及国分之一面力奇异远离散化处理，可以得到各子域的代数方程组，依据凝集技术，可得到仅含有子域公共边界及裂纹边界未知量的求解方程组，通过迭代法，可以寻求到每种载荷作用下的裂纹所处的真实状态，然后，由文献「２」中的方法求解界面裂纹的应力强度因子。结果表明，子域边界方法是正确的     

线性硬化材料的界面裂纹裂尖弹塑性应力场

由全量理论的弹塑性本构方程出发，提出了一种求线性硬化材料裂纹问题的应力函数解法，并求得了线性硬化材料界面裂纹裂尖附近的弹塑性应力场，通过对扩张的Ｄｕｎｄｕｒｓ异材参数β的讨论分析了应力场的振荡奇异性。     

尖端具有线性粘着力作用的加层空间的界面裂纹对稳态弹性波的散射

本文研究一类粘着型界面裂纹的弹性波散射问题．文中利用积分变换和积分方程方法推导了确定这类问题的奇异积分方程组．采用围道积分技术和切比雪夫多项式展开技术，得到了待定系数的非线性代数方程组．最后本文给出裂纹尖端粘着区的大小和界面应力的数值结果．     

界面裂纹问题中的弹性T项和应力强度因子

研究两相材料有限板含单边界面裂纹的断裂力学特性，对不同的材料组合用广义变分法分析了不同尺寸试件和裂纹长度下的应力强度因子和弹性T项，讨论了材料特性对应力强度因子和弹性T项的作用．分析了试件尺寸和裂纹长度对应力强度因子和弹性T项的影响．     

三向应力状态下材料的力学强度理论

通过对古典强度理论和苏联切略依海尔、巴兰金等人所提出的强度极限曲面的分析,本文提出一个新的见解;并通过强度条件的选择和各项参数的研究,导出了一个计算强度的公式。经过与实验结果比较、分析,证明这一公式计算结果与实际情况比较接近。      

PERSPECTIVES IN MECHANICS OF HETEROGENEOUS SOLIDS

The Microand Nano-mechanics Working Group of the Chinese Society of Theoretical and Applied Mechanics organized a forum to discuss the perspectives,trends,and directions in mechanics of heterogeneous materials in January 2010.The international journal,Acta Mechanica Solida Sinica,is devoted to all fields of solid mechanics and relevant disciplines in science,technology,and engineering,with a balanced coverage on analytical,experimental,numerical and applied investigations.On the occasion of the 30 th anniversary of Acta Mechanica Solida Sinica,its editor-in-chief,Professor Q.S.Zheng invited some of the forum participants to review the state-of-the-art of mechanics of heterogeneous solids,with a particular emphasis on the recent research development results of Chinese scientists.Their reviews are organized into five research areas as reported in different sections of this paper.§I firstly brings in focus on microand nano-mechanics,with regards to several selective topics,including multiscale coupled models and computational methods,nanocrystal superlattices,surface effects,micromechanical damage mechanics,and microstructural evolution of metals and shape memory alloys.§II shows discussions on multifield coupled mechanical phenomena,e.g.,multi-fields actuations of liquid crystal polymer networks,mechanical behavior of materials under radiations,and micromechanics of heterogeneous materials.In §III,we mainly address the multiscale mechanics of biological nanocomposites,biological adhesive surface mechanics,wetting and dewetting phenomena on microstructured solid surfaces.The phononic crystals and manipulation of elastic waves were elaborated in §IV.Finally,we conclude with a series of perspectives on solid mechanics.This review will set a primary goal of future science research and engineering application on solid mechanics with the effort of social and economic development.     

受轴向冲击有限长弹性直杆中应力波引起的分叉问题

研究了有限长理想直杆受阶跃载荷作用的弹性动力屈曲问题。将直杆的屈问题归结为由轴向应力波传播而导致的杆的分叉问题，并考虑了应力波反射的影响。给出了分叉发生的临界条件并对具体实例进行了计算。最后对阶跃载荷及脉冲载荷对杆的动力屈曲的影响进行了讨论。     

THEORETICAL MODEL OF EFFECTIVE STRESS COEFFICIENT FOR ROCK/SOIL-LIKE POROUS MATERIALS

Physical mechanisms and influencing factors on the effective stress coefficient for rock/soil-like porous materials are investigated, based on which equivalent connectivity index is proposed. The equivalent connectivity index, relying on the meso-scale structure of porous material and the property of liquid, denotes the connectivity of pores in Representative Element Area （REA）. If the conductivity of the porous material is anisotropic, the equivalent connectivity index is a second order tensor. Based on the basic theories of continuous mechanics and tensor analysis, relationship between area porosity and volumetric porosity of porous materials is deduced. Then a generalized expression, describing the relation between effective stress coefficient tensor and equivalent connectivity tensor of pores, is proposed, and the expression can be applied to isotropic media and also to anisotropic materials. Furthermore, evolution of porosity and equivalent connectivity index of the pore are studied in the strain space, and the method to determine the corresponding functions in expressions above is proposed using genetic algorithm and genetic programming. Two applications show that the results obtained by the method in this paper perfectly agree with the test data. This paper provides an important theoretical support to the coupled hydro-mechanical research.     

轴向冲击载荷作用下锥壳中弹性应力波传播的计算和实验研究

本文利用有限元分析和模型实验研究了在轴向冲击载荷作用下,锥壳中弹性应力波的传播、计算和实验结果表明,结构中存在着弹性纵波和弹性弯曲波的传播,它们传播的速度各不相同,使壳面承受不同的应力状态;讨论了纵波和弯曲波随壳面的衰减;实验指出,由于边界的影响,即使纵波的反射也会产生新的反射弯曲波沿锥面传播。     

岩石钻爆开挖中预裂缝的隔震效果分析

通过应力波与由节理刚度系数描述的预裂缝的相互作用分析，考虑预裂缝在爆炸应力波作用下的闭合效应及预裂缝充水等条件下，研究了预裂缝的隔震机制与隔震效果，从而为岩石开挖过程中周边控制爆破方式的优选提供了理论依据。     

特征线法在三维弹／粘塑性波数值解析中的应用

根据广义特征理论建立了求解三维非线性应力波传播问题的特征关系式,并采用特征线法对纵向冲击载荷下弹／粘塑性矩形截面棒的三维应力波传播过程进行了数值模拟。     

Spalding公式在脊状表面湍壁摩擦力测量中的应用

在低速风洞中来流速度一定的情况下使用IFA300恒温热线风速仪测量了光滑表面和两种不同尺寸的脊状表面湍流边界层平均速度分布剖面,并验证了试验段湍流发展的充分性;通过应用Spalding壁面公式使用最小二乘法精准拟合了实验测量的边界层内层速度分布曲线,得到了湍流边界层壁面摩擦速度并进一步求得湍流壁面摩擦应力,较准确地计算出脊状表面的虚拟原点位置,并通过与对数律公式拟合结果比较分析,证实了该方法更加准确有效. 最后分别计算了3种实验模型的湍流边界层动量损失厚度. 通过对比脊状表面与光滑表面动量损失厚度和壁面摩擦应力,反映了动量损失厚度的大小与壁面摩擦应力的大小具有一致性,充分证实了脊状表面在湍流中具有一定的减阻效果.      

等压比热在基于壁面放电的激波控制中的影响

放电等离子体对流动的控制机理可按热效应和非热效应分为两大类,其中放电等离子体的热效应对流场中激波结构有着明显的控制作用. 目前在放电等离子体热激励对激波控制的数值模拟过程中,通常采用等效热源的方式来实现放电的热效应,数值模拟和实验的结果显示放电产生的局部温度可达到上万度. 如果数值模拟的过程中没有考虑到气体等压比热随温度的非线性变化,计算得到的结果是有失真实性的. 本文以5 马赫的超音速进气道为平台,对基于壁面放电的激波控制过程进行了数值模拟. 选取了随温度非线性变化的等压比热,并且将其结果与定等压比热的计算结果进行了对比. 结果发现:(1) 两种等压比热下,计算结果显示放电热激励在激波控制上都有着显著的效果;(2) 两种计算结果在模拟与温度相关的参数(温度、马赫数和总压恢复系数)上的差别非常明显. 因此,为了获得壁面放电对激波控制更真实的计算结果,必须考虑到等压比热随温度发生非线性变化效应的影响.      

弹性圆柱壳在轴向应力波传播过程中的非对称屈曲

讨论弹性圆柱壳端部受冲击载荷作用，在应力波传播过程中的非对称屈曲问题。通过求解扰动方程得到了动态屈曲的分叉条件、临界载荷和屈曲模态。数值结果表明，当壳壁厚不很薄时，轴对称屈曲临界载荷比非对称临界载荷高；反之，轴对称临界载荷会比非对称临界载荷低。不同的冲击载荷，屈曲模态也将不同。     

两种各向异性材料界面周期裂纹的反平面问题

研究两种各向异性材料界面含周期裂纹的反平面剪切问题，运用复变函数方法，获得了封闭形式解答，并给出了应力强度因子公式。从本文解签的特殊情形，可直接导出均匀各向异性材料共线裂纹，两种各向同性材料界面裂纹的相应问题公式。     

双拉试样裂纹扩展过程中的应力强度因子计算

论文将使用一种界面单元来解决二维裂纹的静态扩展问题.这种界面单元基于虚拟裂纹闭合法,利用商业有限元软件ABAQUS的用户自定义单元UEL功能,发展为界面断裂单元,计算应变能释放率(GⅠ和GⅡ).在裂纹尖端的两个节点间设置一个特殊刚度的弹簧,并引入哑节点计算裂纹尖端后面的张开位移和裂纹尖端前面的虚拟裂纹扩展量.采用这种单元计算应变能释放率时不需要使用奇异单元或折叠单元,不会出现收敛问题,也不需要复杂的后续处理.因此,采用这种断裂单元分析二维裂纹扩展问题是方便的、高效率的,而且也能得到可靠的精度.