Multiple scattering of electro-elastic waves from a buried cavity in a functionally graded piezoelectric material layer

This paper presents a theoretical method to investigate the multiple scattering of electro-elastic waves and the dynamic stress around a buried cavity in a functionally graded piezoelectric material layer bonded to a homogeneous piezoelectric material. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions around the cavity. The image method is used to satisfy the mechanical and electrically short conditions at the free surface of the structure. According to the analytical expression of this problem, the numerical solutions of the dynamic stress concentration factor around the cavity are presented. The effects of the piezoelectric property, the position of the cavity in the layer, the incident wave number and the material properties on the dynamic stress around the cavity are analyzed. Analyses show that the piezoelectric property has great effect on the dynamic stress in the region of higher frequencies, and the effect increases with the decrease of the thickness of FGPM layer. If the material properties of the homogeneous piezoelectric material are greater than those at the surface of the structure, the dynamic stress resulting from the piezoelectric property is greater. The effect material properties at the two boundaries of FGPM layer on the distribution of dynamic stress around the cavity is also examined.     

Effective property of piezoelectric composites containing coated nano-elliptical fibers with interfacial debonding

Based on both the spring layer interface model and the Gurtin-Murdoch surface/interface model, the anti-plane shear problem is studied for piezoelectric composites containing coated nano-elliptical fibers with imperfect interfaces. By using the complex function method and the technique of conformal mapping, the exact solutions of the electroelastic fields in fiber, coating, and matrix of piezoelectric nanocomposites are derived under far-field anti-plane mechanical and in-plane electrical loads. Furthermore, the generalized self-consistent method is used to accurately predict the effective electroelastic moduli of the piezoelectric nanocomposites containing coated nano-elliptical fibers with imperfect interfaces. Numerical examples are illustrated to show the effects of the material constants of the imperfect interface layers, the aspect ratio of the fiber section, and the fiber volume fraction on the effective electroelastic moduli of the piezoelectric nanocomposites. The results indicate that the effective electroelastic moduli of the piezoelectric nanocomposites can be significantly reduced by the interfacial debonding, but it can be improved by the surface/interface stresses at the small scale, which provides important theoretical reference for the design and optimization of piezoelectric nanodevices and nanostructures.     

Saint-Venant torsion analysis of bars with rectangular cross-section and effective coating layers

This paper investigates the torsion analysis of coated bars with a rectangular cross-section. Two opposite faces of a bar are coated by two isotropic layers with different materials of the original substrate that are perfectly bonded to the bar. With the Saint-Venant torsion theory, the governing equation of the problem in terms of the warping function is established and solved using the finite Fourier cosine transform. The state of stress on the cross-section, warping of the cross-section, and torsional rigidity of the bar are evaluated. Effects of thickness of the coating layers and material properties on these quantities are investigated. A set of graphs are provided that can be used to determine the coating thicknesses and material properties so as to keep the maximum von Mises stress on the cross-section below an allowable value for effective use of the coating layer.     

Dynamic Stress Resulting from a Plane Compressional Wave in Two-particle Reinforced Composites

In this paper, based on the theory of elastodynamics, the multiple scattering of elastic waves and dynamic stress in multiparticle reinforced composites is investigated, and the analytical solution of this problem is obtained. By using the wave function expansion method, the expressions of total wave fields in each medium are presented. The addition theorem of spherical Bessel functions is employed to accomplish the translation for different local coordinate systems. According to the continuous boundary conditions around the particles, the expanded mode coefficients are determined. As an example, the variation of dynamic stress concentration factors at the interface between the particles and the matrix under different parameters is analyzed. It can be seen from the results that when the incident frequency is different, the effect of the distance between the centers of the particles on the dynamic stress varies greatly. Only when the distance is greater than a certain number can its effect be ignored. When the distance is fixed, the effect of material properties on dynamic stress is also examined.     

Interaction between edge dislocations and amorphous interphase in carbon nanotubes reinforced metal matrix nanocomposites incorporating interface effect

Dislocations mobility and stability in the carbon nanotubes (CNTs)-reinforced metal matrix nanocomposites (MMNCs) can significantly affect the mechanical properties of the composites. However, current processing techniques often lead to the formation of coated CNT (amorphous interphase exists between the reinforcement and metal matrix), which have large impact upon the image force exerting on dislocations. Even though the importance of the interphase zone formed in metal matrix composites has been demonstrated by many studies for elastic properties, the influence of interphase on the local elastoplastic behavior of CNT-reinforced MMNCs is still an open issue. This paper puts forward a three-phase composite cylinder model with new boundary conditions. In this model, the interaction between edge dislocations and a coated CNT incorporating interface effect is investigated. The explicit expressions for the stress fields and the image force acting on an edge dislocation are proposed. In addition, plastic flow occurring around the coated reinforcement is addressed. The influences of interface condition and the material properties of coated CNT on the glide/climb force are clearly analyzed. The results indicate that the interface effect becomes remarkable when the radius of the coated reinforcement is below 10 nm. In addition, different from the traditional particles, the coated CNT attracts the adjacent edge dislocations, causing pronounced local hardening at the interface between the interphase and the metal matrix under certain conditions. It is concluded that the presence of the interphase can have a profound effect on the local stress field in CNT-reinforced MMNCs. Finally, the condition of the dislocations stability and the equilibrium numbers of dislocations at a given size grain are evaluated for considering the interface effect.     

粗糙面在梯度表面层上滑动接触的应力分布

对粗糙面在梯度表面层上的滑动过程进行应力分布研究,以模拟实际摩擦过程中,考虑塑性变形情况下,梯度覆层体中的应力分布规律,同时与均质体及单覆层体进行比较研究,分析了在表面载荷相同时滑动接触的应力分布。结果表明覆层体出现塑性变形后,在接触表面上的压力分布与弹性变形时有很大变化,在界面处梯度层的应力分布比单层膜更为理想,其应变梯度也较小;受相同表面载荷作用下产生塑性变形时,梯度层膜在基体产生塑性变形较小     

SH波与界面多圆孔的散射及动应力集中

研究了平面SH波对相邻多个界面圆孔的散射及其动应力集中,为了求解,首先利用复变函数和多极坐标方法构造了在含有多个半圆形缺口的弹性半空间,水平面上任一点随时间谐和出平面线源载荷作用时失主移,邓Green函数,且采用“契合”模型,推导了SH波对相邻多个界面圆孔散射的定解积分方程组,进而求得圆孔附近的动应力系数,作为算例,讨论了具有两个界面圆孔对SH波的散射及其相互影响,给出了孔附近的动应力分布曲线。     

SURFACE STRESS EFFECT IN MECHANICS OF NANOSTRUCTURED MATERIALS

This review article summarizes the advances in the surface stress effect in mechanics of nanostructured elements,including nanoparticles,nanowires,nanobeams,and nanofilms,and heterogeneous materials containing nanoscale inhomogeneities.It begins with the fundamental formulations of surface mechanics of solids,including the definition of surface stress as a surface excess quantity,the surface constitutive relations,and the surface equilibrium equations.Then,it depicts some theoretical and experimental studies of the mechanical properties of nanostructured elements,as well as the static and dynamic behaviour of cantilever sensors caused by the surface stress which is influenced by adsorption.Afterwards,the article gives a summary of the analytical elasto-static and dynamic solutions of a single as well as multiple inhomogeneities embedded in a matrix with the interface stress prevailing.The effect of surface elasticity on the diffraction of elastic waves is elucidated.Due to the difficulties in the analytical solution of inhomogeneities of complex shapes and configurations,finite element approaches have been developed for heterogeneous materials with the surface stress.Surface stress and surface energy are inherently related to crack propagation and the stress field in the vicinity of crack tips.The solutions of crack problems taking into account surface stress effects are also included.Predicting the effective elastic and plastic responses of heterogeneous materials while taking into account surface and interface stresses has received much attention.The advances in this topic are inevitably delineated.Mechanics of rough surfaces appears to deserve special attention due to its theoretical and practical implications.Some most recent work is reviewed.Finally,some challenges are pointed out.They include the characterization of surfaces and interfaces of real nanomaterials,experimental measurements and verification of mechanical parameters of complex surfaces,and the effects of the physical and chemical processes on the surface properties,etc.     

无限介质中单个纳米涂层夹杂反平面问题的两个模型

采用零厚度界面模型和界面层模型研究了无限介质中单个纳米涂层圆柱形夹杂的反平面问题,利用复变函数方法获得了两种模型夹杂、涂层和基体内应力场的封闭解析解．研究表明,当界面层模型中的界面相厚度趋于零时,界面层模型可以解析地退化为零厚度界面模型．数值算例分析了界面模量不同取值时应力场的分布和应力的尺度依赖性．本文结果丰富了对纳米夹杂力学行为的认识,并可为直接采用零厚度界面模型有困难的纳米夹杂问题的研究提供有价值的参考．     

动力损伤后的脆性岩石静力蠕变断裂模型研究

应力波动力扰动下脆性岩石的静力蠕变特性,对深部地下工程围岩变形的评价有重要的实践意义.动力载荷作用导致的局部细观裂纹损伤严重影响脆性岩石蠕变力学行为.基于细观裂纹扩展与应力关系模型、动力扰动损伤演化函数、静动力载荷演化路径函数与黏弹性本构模型,提出一种应力波动力扰动下脆性岩石蠕变断裂特性的宏细观力学模型.其中动力损伤通过控制岩石内部细观裂纹数量变化实现.模型描述了应力波动力扰动下岩石的应变时间演化曲线,解释了岩石动力扰动下蠕变失效特性.研究了不同应力波幅值及周期影响下的脆性岩石应变-时间关系曲线,并通过试验结果验证了模型的合理性.讨论了动力损伤变化形式,突变发生时刻,突变量的大小对岩石蠕变失效特性的影响.分析了应力波幅值、周期对岩石动态动力损伤效应以及蠕变失效特性的影响.主要研究结果:动力损伤的变化值越大,岩石蠕变失效发生时间越短.冲击载荷扰动期间,动力损伤发生的时刻及增加的形式,对动力扰动后的岩石应变及蠕变破坏时间影响很小.动力损伤变化量随应力波幅值增加、周期减小而加速增大.应力波幅值越大、周期越小,岩石发生蠕变失效时间越短.     

薄膜涂层材料中的广义瑞利波

基于弹性动力学的线性理论，建立了涂层材料中广义瑞利波传播的理论分析模型，并 且由波动方程和边界条件推导了波的频散方程．分析了慢层和快层对相速度频散的影响，给 出了不同层厚-波长比和不同涂层-基体密度比情况下广义瑞利波相速度的理论解．算例分 析分别比较了慢层和快层结构中波的相速度、群速度，以及随深度衰减的位移与应力振 幅．另外，相速度曲线和位移振幅曲线与文献中给出的结果吻合，验证了理论模型和分析过 程的正确性．     

Transient response of an interface crack between dissimilar piezoelectric layers under mechanical impacts

Using the integral transform and the Cauchy singular integral equation methods, the problem of an interface crack between two dissimilar piezoelectric layers under mechanical impacts is investigated under the permeable electrical boundary condition on the crack surface. The dynamic stress intensity factors (DSIFs) of both mode-I and II are determined. The effects of the crack configuration and the combinations of the constitutive parameters of the piezoelectric materials on the dynamic response are examined. The numerical calculation of the mode-I plane problem indicates that the DSIFs may be retarded or accelerated by specifying different combinations of material parameters. In addition, the parameters of the crack configuration, including the ratio of the crack length to the layer width and the ratio between the widths of two layers, exert a considerable influence on the DSIFs. The results seem useful for design of the piezoelectric structures and devices of high performance.     

Dynamic stress intensity factor of a crack perpendicular to the weak-discontinuous interface in a nonhomogeneous coating–substrate structure

A mechanical model was established for the antiplane dynamic fracture problem of a functionally graded coating–substrate structure with a coating crack perpendicular to the weak-discontinuous interface. The problem was reduced to a Cauchy singular integral equation by the methods of Laplace and Fourier integral transforms. Erdogan’s collocation method and the Laplace numerical inversion proposed by Miller and Guy were used to calculate the dynamic stress intensity factors. Three conclusions were drawn through parametric studies: (a) unlike the conclusion drawn for an interfacial crack, reducing the weak discontinuity of the interface will not necessarily decrease the dynamic stress intensity factor (DSIF) of the coating crack perpendicular to the interface; (b) increasing the stiffness of the substrate when that of the coating is fixed, or decreasing the stiffness of coating when that of the substrate is fixed, will be beneficial for the reduction of the DSIF of a coating crack perpendicular to the interface; and (c) the free surface has a greater influence on the DSIF than the interface does, and the effect of the interface on the DSIF is greater than that of the material stiffness in the crack-tip region.     

Molecular dynamics study on mechanics of metal nanowire

The new concept of using nanowires as building blocks for logic and memory circuits makes it very necessary to fully understand the mechanical behaviors of these nanowires. Embedded-atom method is employed to carry out three-dimensional molecular dynamics simulations of the mechanical properties of rectangular cross-section copper nanowire. A stable free-relaxation state and the stress–strain relation of nanowire under extension are obtained. The elastic modulus, yielding strength and deformation are studied. The surface effect, size effect, and temperature effect on the extension property of metal nanowire are discussed in detail. The simulation results from our present work show that at nanoscale surface atoms play an important role on the mechanical behaviors of nano-structures. This study of mechanical properties of metal nanowires will be helpful to the design, manufacture and manipulation of nano-devices.     

SH波作用下界面任意形状孔洞附近的动应力集中

采用Green函数和复变函数法求解了平面SH波在界面任意形状孔洞上的散射问题.首先,取含有任意形状凹陷的弹性半空间,在其水平表面上任意一点承受时间谐和的反平面线源荷载作用时的位移场作为Green函数.然后,按契合方式构造出界面任意形状孔洞对SH波的散射模型,利用所得Green函数按界面位移连续条件建立求解问题的定解积分方程组,求解界面孔附近的动应力集中系数.最后,给出了界面上椭圆孔和方孔边缘动应力集中系数的数值结果,并讨论了不同介质参数和孔洞形状对孔附近动应力集中系数的影响.     

考虑界面应力时纳米涂层纤维增强复合材料的有效力学性能

基于Gurtin-Murdoch表/界面理论和广义自洽方法,获得了考虑界面应力时纳米涂层纤维增强复合材料有效反平面剪切模量的闭合形式解。讨论了涂层的壁厚、力学性能和界面性能对复合材料有效性能的影响。结果显示：在纳米尺度范围内,复合材料的有效反平面剪切模量受纳米涂层的尺寸影响显著。纤维体积分数一定时,涂层壁厚越大,纤维半径越小,有效反平面剪切模量与经典结果偏差越大。纤维刚度和涂层界面性能对复合材料有效模量的影响也取决于涂层刚度,非常软或非常硬的涂层都大大限制了纤维刚度对复合材料有效模量的贡献,过高的涂层刚度屏蔽了纳米复合材料表/界面效应的影响。     

Dynamic stress of a circular cavity buried in a semi-infinite functionally graded piezoelectric material subjected to shear waves

The paper presents a theoretical method to investigate the multiple scattering of shear waves and dynamic stress around a circular cavity in a semi-infinite functionally graded piezoelectric material. The analytical solutions of wave fields are expressed by employing wave function expansion method and the expanded mode coefficients are determined by satisfying the boundary conditions of the cavity. Image method is used to satisfy the free boundary condition of the semi-infinite structure. According to the analytical expression of this problem, the numerical solutions of the dynamic stress concentration factor around the cavity are presented. The effects of the piezoelectric property, the buried depth of the cavity, the incident wave number and the nonhomogeneous parameter of materials on the dynamic stress around the cavity are analyzed. Analyses show that the piezoelectric property has great effect on the dynamic stress in the region of intermediate frequency and the effect increases with increasing wave number. When the nonhomogeneous parameter of materials is less than zero, it has less influence on the maximum dynamic stress around the cavity; however, it has greater influence on the distribution of the dynamic stress around the cavity. When the nonhomogeneous parameter of materials is greater than zero, it has greater influence on both the maximum dynamic stress and the distribution of dynamic stress around the cavity, especially in the case that the buried depth is comparatively small.     

SH波对双相介质界面附近圆形孔洞的散射

建立了求解平面SH波对双相介质界面附近圆形孔洞散射与动应力集中的一种分析方法．利用复变函数与多极坐标的方法构造了一个Green函数，它是在含有圆形孔洞的弹性半空间的水平面上任一点上作用时间谐和的出平面线源荷载的位移解．利用“契合”模型，并根据界面上位移连续性条件，建立了求解SH波对双相介质界面附近圆形孔洞散射的具有弱奇异性的第一类Fredholm型积分方程．给出了圆孔周边上动应力集中系数的表达式．作为算例，分析了在界面一侧或界面两侧附近具有圆形孔洞时SH波的散射，并讨论了入射波波数、不同的材料组合以及孔心至界面的距离对动应力集中的影响．     

Analysis of stress concentration around a spheroidal cavity under asymmetric dynamic loading

The fracture and fatigue properties of porous materials are strongly influenced by stress concentrations around the pores. In addition, failure of structural components initiates at locations of high stress concentration which is often caused by holes, inclusions or other discontinuities. In view of this, the stress concentration around a spheroidal cavity embedded in an elastic medium is studied under dynamic loading conditions. While solutions abound for static loads, only limited solutions exist for dynamic loads. The stress field around a spheroidal cavity is determined by using a hybrid methodology that combines the finite element technique with a spherical wave function expansion method. The stress concentrations within the matrix are found to be dependent on the frequency of excitation, aspect ratio of the cavity and the Poisson’s ratio of the matrix. The study reveals that dynamic stress concentrations can reach much higher values than those encountered under static loading.     

多孔泡沫牺牲层的动态压溃及缓冲吸能机理研究

本文对强动载荷下多孔泡沫牺牲层的动态压溃行为及缓冲吸能机理进行了研究. 基于刚性-理想塑性-锁定(R-PP-L)及刚性-塑性硬化(R-PH)两类多孔泡沫材料本构, 建立了强动载荷下多孔泡沫牺牲层动态响应的理论分析模型, 分析了一维冲击波在多孔泡沫牺牲层中的传播规律; 利用Voronoi方法建立了多孔泡沫牺牲层的二维细观有限元模型, 获得了冲击载荷下多孔泡沫牺牲层的变形模式和动态响应曲线, 讨论了多孔泡沫材料的层间界面效应对多孔泡沫牺牲层缓冲吸能的影响. 研究结果表明, 考虑多孔泡沫材料塑性硬化影响的理论分析模型能够预测入射波在远端的反射及对多孔泡沫牺牲层的二次压缩过程和端部应力增强现象; 相比较存在界面的多孔泡沫牺牲层, 连续设计的多孔泡沫牺牲层可增强其缓冲吸能能力, 但在界面处增加设计刚性面板则能够降低界面胞元不完整对缓冲吸能的影响; 相同冲量载荷下, 端部应力峰值随冲击能量增大而增大, 而端部冲击波的反射可能是端部应力增强的主要诱因.