Analysis of stress field in a single anisotropic diamond/square shaped inclusion using the volume integral equation method and the numerical equivalent inclusion method

A volume integral equation method (VIEM) is used to study elastostatic problems in an unbounded elastic solid containing a single diamond/square shaped inclusion subject to uniform tensile stress at infinity. The inclusion is assumed to be a long parallel diamond/square cylinder composed of isotropic or anisotropic elastic materials and perfectly bonded to the isotropic matrix. The solid is assumed to be under plane strain on the plane normal to the cylinder. A detailed analysis of the stress field at the interface between the isotropic matrix and the single isotropic/orthotropic diamond/square shaped inclusion is carried out. The effects of a single isotropic/orthotropic diamond/square shaped inclusion on the stress field at the interface between the matrix and the inclusion are investigated in detail. The accuracy of the volume integral equation method for the interfacial stress field is validated and compared by the numerical equivalent inclusion method (NEIM) and the finite element method (FEM) using ADINA. Through detailed analysis of plane elastostatic problems using the parallel volume integral equation method (PVIEM) in an unbounded isotropic matrix with multiple isotropic diamond shaped inclusions under uniform remote tensile loading, it is demonstrated that the volume integral equation method can also be applied to solve general two- and three-dimensional elastostatic problems involving multiple isotropic/anisotropic inclusions whose shape and number are arbitrary.     

Effective Anisotropic Dielectric Properties of Crystal Composites

Transformation fieM method （TFM） is developed to estimate the anisotropic dielectric properties of crystal composites having arbitrary shapes and dielectric properties of crystal inclusions, whose principal dielectric axis are different from those of anisotropic crystal matrix. The complicated boundary-value problem caused by inclusion shapes is circumvented by introducing a transformation electric field into the crystal composites regions, and the effective anisotropic dielectric responses are formulated in terms of the transformation field. Furthermore, the numerical results show that the effective anisotropie dielectric responses of crystal composites periodically vary as a function of the rotating angle between the principal dielectric axes of inclusion and matrix crystal materials. It is found that at larger inclusion volume fraction the inclusion shapes induce profound effect on the effective anisotropic dielectric responses.     

Numerical study of contacts between a flat-ended punch and a half-space embedded with inhomogeneities

This paper presented a numerical approach to solving the problem of a flat-ended punch in contact with a half-space matrix embedded with multiple three dimensional arbitrary-shaped inhomogeneities.Based on the semi-analytical method(SAM)and the equivalent inclusion method,numerical procedures were developed and the effects of inclusion shape and distribution were analyzed.Fast Fourier transform technique was implemented to accelerate the calculation of surface deformation and subsurface stress.Interactions of inter-inclusions and inclusion-matrix were taken into account.Numerical results showed the presence of inhomogeneities(i.e.,microstructures in solids)indeed had a great effect on local contact pressure and a strong disturbance to the subsurface stress field in the vicinity of inclusions.The effects were dependent on the shape and distribution of inclusions and inter-inclusion interactions.The physical significance of this study is to provide an insight into the relation between the material microstructure and its response to the external load,and the solution approach and procedures may find useful applications,for example,the analysis of fatigue and crack propagation for composite materials,prediction of stress field in solids containing material defects,and study of the mechanism of chemical-mechanical polish(CMP)for inhomogeneous materials,etc.     

A general model for hydrogen trapping at the inclusion-matrix interface and its relation to crack initiation

Abstract

The role of non-metallic inclusions in hydrogen-induced failure of structural materials has been a controversial topic for many years. In this paper, hydrogen trapping and its relation to the crack initiation at the inclusion-matrix interfaces are studied by considering the interfacial structure and the interaction between the dissolved hydrogen atoms and the elastic strains produced by lattice matching and misfit dislocations. A model is proposed to analyse the change of interfacial structure with inclusion size and its relation to hydrogen trapping. Hydrogen accumulation at the interfaces is quantitatively analysed. The obtained results are in good agreement with the experimental observations. The multiple factors, such as interfacial structure, chemical composition, elastic properties of matrix and inclusions, crystallographic relationship between inclusions and matrix, inclusion morphology and size, simultaneously control hydrogen trapping. In addition, the mechanism of hydrogen-induced crack initiation at the interface is investigated. A criterion is proposed to determine critical conditions for crack initiation. For the first time, the inherent relationship between hydrogen trapping and hydrogen-induced cracking at the interface is clarified. This work paves a way for an in-depth understanding of the effects of inclusions on hydrogen-induced degradation of mechanical properties.     

Micromechanical modelling of an arbitrary ellipsoidal multi-coated inclusion

The present work aims to provide a general framework to deal with an elementary heterogeneous problem, where the inhomogeneity consists of an n-layered inclusion composed of n concentric ellipsoids made of anisotropic elastic materials. The methodology is based on a combination of Green's function techniques with interface operators, illustrating the stress and strain jump conditions at the interfaces between two adjacent coatings, which are considered perfectly bonded. The model is validated in the case of double-coated spherical inclusions made of isotropic materials, where the obtained analytical results cover the exact solution of Hervé and Zaoui. The model can be applied, after adequate choice of scale-transition methods, to describe the overall behaviour of real composite materials with complex microstructures that are significantly influenced by the presence of interphase layers between constituents (fillers and matrix). Such composites are widely employed in automotive and aerospace industries. As a typical example one can consider a composite with an epoxy matrix reinforced by glass beads coated using a thin soft polymeric phase or syntactic foams particulate composites obtained by filling a polymeric matrix with hollow solid inclusions.     

Scattering of SH-wave by an elliptical inclusion with partial debonding curve in half-space

For the purpose of revealing the dynamic properties of elliptical inclusion in the half-space, solving the problem of scattered SH-wave, the method of ‘conformal mapping’ is used to map an elliptical inclusion into a circular inclusion. The displacement field and the stress field of the elliptical inclusion while bearing out-plane line source load are obtained by Green’s function method. Then, infinite system of linear equations is established by displacement and stress continuous boundary conditions, to solve unknown coefficients of wave function. Finally, the ‘partial debonding curve model’ is constructed, and the equal stress but opposite in direction is applied in the partial debonding curve. It is obtained the total displacement field of the elliptical inclusion with a partially debonding curve in the half-space. Numerical results demonstrate that dynamic stress concentration factor is influenced in the incident angle, the frequency of incident wave, the depth of inclusions and the partial debonding curve angle.     

Surface impedance matrices to model the propagation in multilayered media

The surface impedance matrices in stratified plates made of fluid layers and/or anisotropic absorbing solid layers link the particle velocity field to the stress field at any interface. A surface impedance matrix represents the impedance at a given interface of all the layers located between that interface and one boundary of the medium. For each interface, there are two surface impedance matrices, each one corresponding to one boundary. This notion simplifies the computations of the modal solutions. The number of elements in the matrices involved in the computations is divided by a factor of four in comparison to usual matrix methods. This paper describes the method and presents examples to illustrate its interests and its efficiency where other techniques fail, for instance in the case of modes possessing energy in layers embedded in the structure.     

Scattering from an elliptical cylindrical plasma for electromagnetic waves with wavelength much greater than the dimensions of the plasma cross-section

The distribution of the electric potential inside and outside a cold plasma column with elliptical cross-section when electromagnetic waves scatter from it are obtained. It is assumed that the wavelength of incident wave is much greater than the dimensions of the cross section of the plasma column. The electrical potential inside and outside a magnetized elliptical plasma column for an anisotropic scattering process are obtained. The graphs of the ratio of the electric field inside the plasma and the incident electric field versus the incident angle, the geometrical dimension of the elliptical plasma column and cyclotron frequency are presented separately. Finally, scattering of the same waves from an elliptical cylindrical inhomogeneous isotropic cold plasma is also investigated.     

Elastic field of cylindrical inclusion

The elastic field of a cylindrical inclusion with plane or antiplane transformation strain is found under assumptions of linear isotropic homogeneous theory of elasticity. Different integral expressions are obtained from expressions known for the three-dimensional case and interpreted in terms of the theory of dislocations. The surface integrals correspond to a volume distribution of infinitesimal dislocation dipoles inside the inclusion, the line integrals to a surface distribution of dislocations in the boundary between the inclusion and matrix. The case of a shear transformation in a rectangular region is discussed in more detail in connection with twinning.     

耦合势有限体积法高效模拟各向异性地层中海洋可控源的三维电磁响应

本文基于电场矢势与标势分解的耦合势有限体积法研究建立一套各向异性地层中海洋可控源电磁法的三维响应的高效数值模拟技术.首先引入电场的矢势和标势,将电场分解为无散场和无旋场之和,Maxwell方程转换为关于矢势与标势的混合Helmholtz方程,克服低感应数问题.在此基础上,借助Yee氏交错网格和有限体积法以及非均质单元中等效电导率公式,建立混合Helmholtz方程的离散方程.并采用直接法求解器PARDISO求解离散方程,有效保证在大的求解空间中仍然能够获得电磁场稳定可靠的数值解.此外,在数值模拟中利用差异场技术,克服源的奇异性问题,尽可能提高近场的计算精度.与解析解的对比证明了该算法的有效性.数值模拟结果表明,海洋可控源电磁法沿测线方向的电场,对油气藏的纵向电阻率敏感,对横向电阻率不敏感;对油气藏上方的覆盖层的纵向电阻率和横向电阻率都敏感.     

Elastic wave field computation in multilayered nonplanar solid structures: a mesh-free semianalytical approach

Multilayered solid structures made of isotropic, transversely isotropic, or general anisotropic materials are frequently used in aerospace, mechanical, and civil structures. Ultrasonic fields developed in such structures by finite size transducers simulating actual experiments in laboratories or in the field have not been rigorously studied. Several attempts to compute the ultrasonic field inside solid media have been made based on approximate paraxial methods like the classical ray tracing and multi-Gaussian beam models. These approximate methods have several limitations. A new semianalytical method is adopted in this article to model elastic wave field in multilayered solid structures with planar or nonplanar interfaces generated by finite size transducers. A general formulation good for both isotropic and anisotropic solids is presented in this article. A variety of conditions have been incorporated in the formulation including irregularities at the interfaces. The method presented here requires frequency domain displacement and stress Green's functions. Due to the presence of different materials in the problem geometry various elastodynamic Green's functions for different materials are used in the formulation. Expressions of displacement and stress Green's functions for isotropic and anisotropic solids as well as for the fluid media are presented. Computed results are verified by checking the stress and displacement continuity conditions across the interface of two different solids of a bimetal plate and investigating if the results for a corrugated plate with very small corrugation match with the flat plate results.     

非均质各向异性地层中方位随钻电磁测井响应三维有限体积法数值模拟算法

方位随钻电磁测井是一种能够实时探测地层边界、实现地质导向与井眼成像的新型测井技术. 本文根据方位随钻电磁测井仪器的典型线圈系结构, 首先引入柱坐标系下非均质完全各向异性地层中电流源并矢Green函数, 并利用电磁场叠加原理给出倾斜发射线圈激发的电场以及倾斜接收线圈上感应电动势的计算公式; 然后应用电流源电场并矢Green函数的混合势克服非均质地层中电磁数值模拟的低感应数问题, 通过ρ 和z方向上Lebedev网格设法降低网格节点个数, 并且利用标准化算法确定柱坐标系下非均质单元上的等效电导率. 在此基础上, 用三维有限体积法建立柱坐标系电场混合势的离散方法, 得到一个交错网格上电场矢势和标势大型代数方程, 并用不完全LU分解以及稳定双共轭梯度法确定数值解. 最后, 通过数据模拟结果对算法的有效性进行检验, 并考察钻铤、线圈倾斜角度以及地层各向异性等参数对仪器响应的影响. 数值结果表明: 在柱坐标系下用三维有限体积法的数值模拟算法处理非均质各向异性层中方位随钻电磁测井响应可以得到很好的结果. 钻铤、电导率各向异性、层边界均对方位随钻电磁波测井响应产生较大的影响; 在电阻率较大的地层, 幅度比和相位差响应越小; 发射线圈和接收线圈同时倾斜时, 幅度比和相位差响应受地层的影响更灵敏.     

A Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core

The electro-elastic interaction between a piezoelectric screw dislocation and an elliptical piezoelectric inhomogeneity, which contains an electrically conductive confocal elliptical rigid core under remote anti-plane shear stresses and in-plane electrical load is dealt with. The analytical solutions to the elastic field and the electric field, the interfacial stress fields of inhomogeneity and matrix under longitudinal shear and the image force acting on the dislocation are derived by means of complex method. The effect of material properties and geometric configurations of the rigid core on interfacial stresses generated by a remote uniform load, rigid core and material electroelastic properties on the image force is discussed.     

On the theory of conductivity of anisotropic composites: A linear-concentration approximation of inclusions

A general approach is proposed for calculating the conductivity of anisotropic composites with a low concentration of inclusions of an arbitrary shape. The contribution to effective conductivity [^(s)] _e\hat \sigma _e, which is linear in concentration, is expressed in terms of the polarizability of the inclusion defined in a certain transformed system in which the inclusion is surrounded by an isotropic matrix. A transition to this system is performed using a symmetry transformation that does not change the equations for direct current.     

各向同性紊流能量衰减的大涡模拟

在多重网格驱动的,高效且得到充分验证的有限体积方法的基础上发展了可压缩流大涡模拟的方法.空间离散采用Jameson的中心格式附加二阶和四阶耗散的方法,时间推进则采用了双时间步长的方法.亚格子剪切应力张量和亚格子热通量用Smagorinsky模型进行模拟.通过对各向同性紊流能量衰减的模拟来验证本方法的准确性和高效性,模拟得到的能量谱和紊流动能衰减历程与过滤后的CBC实验数据吻合良好.     

Conduction of the three-dimensional model of a composite with structural anisotropy

The electric conduction of the model of a structurally anisotropic composite that represents an isotropic matrix with disk-shaped inclusions (oblate spheroids) is analytically studied. The disks have the same orientation and their centers are randomly distributed in the composite volume. The cases of dielectric and ideally conducting inclusions are considered. The conduction of the model in a broad concentration range is described by the approximate effective medium method. Conduction in the critical region (in the vicinity of the metal–dielectric phase transition point) is studied using the similarity hypothesis.     

解二维中子输运问题的三角网格配置法

本文研究了二维轴对称中子输运(包括各向同性散射和各向异性散射)问题的一种有限元数值方法。给出了一系列的数值计算结果,并与国内外的SN、间断有限元方法的数值结果及实验结果进行比较,取得了令人满意的结果。     

Effective responses of nonlinear elliptic cylindrical composites

The higher-order dielectric responses of composites composed of weakly nonlinear elliptic cylindrical inclusions randomly embedded in linear media are investigated. The general formulae for effective DC coefficients are newly derived by the average field method up to the ninth order and then applied to analyze the effects of inclusion shapes on the effective response. The results are directly transformed to the quasi-static AC response of the composites under the sinusoidal external electric field with fundamental and third harmonic frequencies. The more general relationships between the effective DC and AC coefficients are established up to the seventh order and third harmonic, which are applicable to all weakly nonlinear isotropic composites.     

Effective parameters of multicomponent dielectrics with hexagonal structure

The effective parameters of a matrix dielectric medium that contains three types of unidirectional cylindrical inclusions forming the hexagonal lattice are calculated. The electric field and the average characteristics of the system are analytically calculable if the concentration of the inclusions is low. Small parameters characterizing the system are indicated, and the general form of the expression for the effective permittivity of anisotropic multicomponent media is presented.     

KDP晶体微纳加工表层杂质对其激光损伤阈值影响的有限元分析

 根据KDP晶体杂质附近的温度场及热应力场理论,分析了微纳加工表层杂质影响下晶体温度场及热应力场的分布情况,发现杂质离子对激光的强吸收作用是造成KDP晶体损伤的主要原因之一,也是影响KDP晶体激光损伤阈值的最主要因素。通过分析还发现杂质半径对晶体的激光损伤阈值也有影响,并得到一个有害的杂质半径,使得杂质吸收能量最多,温度最高。另外杂质种类及杂质含量的不同也会对晶体的激光损伤阈值产生影响。