An exact analysis for mode III cracks between two dissimilar magnetoelectroelastic layers

This paper develops a closed-form solution for an interface crack in a layered magnetoelectroelastic strip of finite width. The strip is subjected to anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for the stress, electric, and magnetic fields, together with their intensity factors, are obtained for two extreme cases of an impermeable and a permeable cracks. The stress intensity factor does not depend on the electromagnetic boundary conditions assumed for the crack. However, the electrically and magnetically permeable boundary conditions on the crack profile have a significant influence on the crack-tip electromagnetic field intensity factors. Solutions for some special cases, such as a central crack, an edge crack, two symmetric collinear cracks, and a row of collinear interface cracks, are also obtained in closed forms. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 763–784, November–December, 2008.     

A new boundary element method for the solution of plane steady-state thermoelastic fracture mechanics problems

An efficient numerical technique is developed for plane, homogeneous, isotropic, steady-state thermoelasticity problems involving arbitrary internal smooth and/or kinkedcracks. The thermal stress intensity factors and relative crack surface displacements due to steady-state temperature distributions are determined and compared to available solutions obtained by other methods. In these analyses the thermal boundary conditions across the crack surface are assumed to be insulated. The present approach involves coupling the direct boundary integral equations to newly developed crack integral equations.     

Stress intensity factors for three cracks at the interfaces of a graded layer bonding two different materials

We consider two dissimilar elastic half-planes bonded by a nonhomogeneous elastic layer in which there is one crack at the lower interface between the elastic layer and the lower half-plane and two cracks at the upper interface between the elastic layer and the upper half-plane. The stress intensity factors for these three cracks are solved for when tension is applied perpendicular to the interface cracks. The material properties of the bonding layer vary continuously between those of the lower half-plane and those of the upper half-plane. The differences in the crack surface displacements are expanded in a series of functions that are zero outside the cracks. The unknown coefficients in the series are solved by the Schmidt method so as to satisfy the conditions inside the cracks. The stress intensity factors are calculated numerically for selected crack configurations.     

双材料接合半无限体三维矩形界面裂纹应力强度因子分析

基于体积力法,研究了双材料接合半无限体三维矩形界面裂纹的应力强度因子问题．在数值计算中,未知的体积力密度采用基本密度函数和多项式乘积的形式来近似,其中基本密度函数是根据界面裂纹应力的振荡奇异性来选取的．计算结果表明,基于本算法得到的数值结果其收敛精度和计算误差都是令人满意的．算例中,给出了应力强度因子随矩形形状及双材料参数的变化规律．     

Fracture of a piezoelectric fiber/elastic matrix composite

A piezoelectric fiber/elastic matrix system subjected to axially symmetric mechanical and electric loads is considered. The fiber contains a penny-shaped crack located at its center perpendicularly to the fiber. By using the Fourier and Hankel transforms, the problem is reduced to the solution of an integral equation. Numerical solutions for the crack tip fields are obtained for various crack sizes and different fiber volume fractions. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 301–318, May–June, 2006.     

On the problem of determining the parameters of a layered elastic medium and an impulse source

Considering the linear system of elasticity equations describing the wave propagation in the half-space ? ₊ ³ = {x ∈ ?³ | x ₃ > 0} we address the problem of determining the density and elastic parameters which are piecewise constant functions of x ₃. The shape is unknown of a point-like impulse source that excites elastic oscillations in the half-space. We show that under certain assumptions on the source shape and the parameters of the elastic medium the displacements of the boundary points of the half-space for some finite time interval (0, T) uniquely determine the normalized density (with respect to the first layer) and the elastic Lamé parameters for x ₃ ∈ [0, H], where H = H(T). We give an algorithmic procedure for constructing the required parameters.     

一类复合材料焊接的界面裂纹问题

利用复变方法和解析函数边值问题的基本理论，研究一类复合材料焊接线上出现裂纹的平面弹性基本问题，笔者通过适当的函数分解和积分变换，将寻找复应力函数的问题转化为求解一正而型奇异积分方程，并借助积分方程理论给出了方程的求解方法。     

A new approach to the flash technique for the remote sensing of layered materials

A radically new technique of frontal monitoring, the sliding tangent method, is proposed, which makes it possible to determine the instant when the temperature regime on the surface of the body under study becomes regularized. Together with the regression analysis of the time-temperature relation for the surface, represented as a time series, this method provides a handy way for remote measuring of the thermophysical properties of material bodies to a high accuracy. The method is particularly attractive for investigating objects in vacuum, at high pressures and temperatures, and in other hostile conditions. This technique is of primary importance when the back side of the object to be investigated is inaccessible. Furthermore, any change at the surface or the back of a body can be detected remotely and nondestructively. The time and geometrical limitations for the suggested method are indicated.Tomsk Polytechnic Institute, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 393–400, May–June, 1999.     

具有双裂纹的弹性复合材料板承受剪切冲击时的动应力强度因子

本文研究了两个材半限弹性的接合面附近存在与接合面平行的双裂纹，并承受剪切冲击时的瞬态应力，运用付里叶（Ｆｏｕｒｉｅｒ）和拉普拉斯（Ｌａｐｌａｃｅ）变换，将问题归结为求解二元积分方程，求解时将裂纹所在面上，下的位移差展成级数，并让其自动满足裂纹面外的位移差为零的条件，利用裂纹面上的边界条件和施密特（Ｓｃｈｍｉｄｔ）方法求解级数中的待定系数，在拉普拉斯像空间中，求得动应力强度因子，并将其数值地逆变换至     

Designing of layered rod structures from viscoelastic materials at a given service life

The problem on the rational design of a layered rod structure subjected to force and temperature actions under the conditions of creep is considered. The linear hereditary theory is used for the viscoelastic materials of layers. The rods are packages of several homogeneous layers with a rectangular cross section. The variable geometrical parameters of the rods are determined from the energy equal-strength condition at a given in stant of time. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 581–594, September–October, 2007.     

用界面单元法分析复合材料界面力学性能

本文利用界面单元的固有特性，将其用来模拟复合材料中纤维与基体之间的界面特征，计算了一个沿Ｘ轴方向纤维周期排列的单尾板，在横向载荷作用下的应力分布问题．给出了三相（纤维、基体和界面）特性各种配比时应力分布等高线图以及通过界面时径向应力σｒ的变化情况，反映了界面特性对应力分布的影响．     

The direct and inverse problem for an inclusion within a heat-conducting layered medium

This paper is concerned with the problem of heat conduction from an inclusion in a heat transfer layered medium. Making use of the boundary integral equation method, the well-posedness of the forward problem is established by the Fredholm theory. Then an inverse boundary value problem, i.e. identifying the inclusion from the measurements of the temperature and heat flux on the accessible exterior boundary of the medium is considered in the framework of the linear sampling method. Based on a careful analysis of the Dirichlet-to-Neumann map, the mathematical fundamentals of the linear sampling method for reconstructing the inclusion are proved rigorously.     

Non-local theory solution of two collinear mode-I cracks in piezoelectric materials

In this paper, the basic solution of two collinear cracks in a piezoelectric material plane subjected to a uniform tension loading is investigated by means of the non-local theory. Through the Fourier transform, the problem is solved with the help of two pairs of integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the integral equations, the jumps of displacements across the crack surfaces are directly expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the interaction of two cracks, the materials constants and the lattice parameter on the stress field and the electric displacement field near crack tips. Unlike the classical elasticity solution, it is found that no stress and electric displacement singularities are present at crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to using the maximum stress as a fracture criterion in piezoelectric materials.     

The effect of hydrostatic pressure on the crack resistance of particulate reinforced composite materials

The effect of hydrostatic pressure on the fracture toughness of disperse-reinforced composite materials is investigated. It is shown that increased hydrostatic pressure leads to an increase in the critical value of the stress intensity factor and, as a consequence, to an increase in the crack propagation rate. In this case, the pressure-time analogy method can be used to describe the effect of hydrostatic pressure on the characteristics of the crack resistance. This method enables us to represent the experimental data obtained in the form of a generalized dependence of the fracture toughness on the reduced loading rate. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 1, pp. 121–126, January–February, 2000.     

An anisotropic flow law for incompressible polycrystalline materials

New and explicit anisotropic constitutive equations between the stretching and deviatoric stress tensors for the two- and three-dimensional cases of incompressible polycrystalline materials are presented. The anisotropy is assumed to be driven by an Orientation Distribution Function (ODF). The polycrystal is composed of transversally isotropic crystallites, the lattice orientation of which can be characterized by a single unit vector. The proposed constitutive equations are valid for any frame of reference and for every state of deformation. The basic assumption of this method is that the principle directions of the stretching and of the stress deviator are the same in the isotropic as well as in the anisotropic case. This means that the proposed constitutive laws are able to model the effects of anisotropy only via a change of the fluidity due to a change of the ODF. Such an assumption is justified to guarantee that, besides knowledge of the parameters involved in the isotropic constitutive equation, the anisotropic material response is completely characterized by only one additional parameter, a type of enhancement factor. Explicit comparisons with experimental data are conducted for Ih–ice. Dedicated to Prof. L.W. Morland on the occasion of his 70^th birthday Received: July 6, 2004; revised: November 8, 2004     

Homogenization of the layered medium equation

A new partial differential equation to be called the layered medium equation is introduced, and it is proved that certain relevant initial or periodic boundary conditions give well-posed problems. Then, the homogenized limit of the layered medium equation is studied. It is shown to be preserved in limit in the limit in the physical problem in which the coefficients that arise from the dielectric layer are both proportional to thickness. Otherwise, a non-local problem is obtained as the limiting form     

各向异性材料界面周期刚性线夹杂的反平面问题

研究了两种各向异性材料界面含周期分布刚性线夹杂的反平面剪切问题。运用复变函数方法,获得了封闭形式解答,并给出了刚性线尖端应力场公式,从该文解答的特殊情形,可直接导出各向同性材料界面以及均匀各向异性材料中相应问题的公式,其极限情形与已有的结果吻合。     

Interlaminar fracture and low-velocity impact of carbon/epoxy composite materials

The interlaminar fracture and the low-velocity impact behavior of carbon/epoxy composite materials have been studied using width-tapered double cantilever beam (WTDCB), end-notched flexure (ENF), and Boeing impact specimens. The objectives of this research are to determine the essential parameters governing interlaminar fracture and damage of realistic laminated composites and to characterize a correlation between the critical strain energy release rates measured by interlaminar fracture and by low-velocity impact tests. The geometry and the lay-up sequence of specimens are designed to probe various conditions such as the skewness parameter, beam volume, and test fixture. The effect of interfacial ply orientations and crack propagation directions on interlaminar fracture toughness and the effect of ply orientations and thickness on impact behavior are examined. The critical strain energy release rate was calculated from the respective tests: in the interlaminar fracture test, the compliance method and linear beam theory are used; the residual energy calculated from the impact test and the total delamination area estimated by ultrasonic inspection are used in the low-velocity impact test. Results show that the critical strain energy release rate is affected mainly by ply orientations. The critical strain energy release rate measured by the low-velocity impact test lies between the mode I and mode II critical strain energy release rates obtained by the interlaminar fracture test. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 195–214, March–April, 2000.     

Some typical behaviors of weak solutions of layered proous media equation

This paper is the continuation of [2]. Some typical behaviors of weak solutions of layered porous media equations with boundary conditions will be discussed in this paper. For example, asymptotically, the saturated regions can appear only either near the layered interface, or near the boundaries. The necessary and sufficient conditions for the occurrence of such phenomena will be given.     

Electromagnetic scattering theorems for interior dipole excitation of a layered obstacle

A layered scatterer is excited by a time‐harmonic spherical electromagnetic wave, generated by a dipole located either in the interior or in the exterior of the scatterer. The scatterer's core may be perfect conducting, impedance or dielectric. This paper initiates the investigation of scattering theorems corresponding to the excitation of a layered scatterer by a dipole in its interior. We establish reciprocity and general scattering theorems relating the total electric fields with the corresponding far‐field patterns. The optical theorem, relating the scattering cross‐section with the electric field in the layer containing the dipole, is recovered as a corollary of the general scattering theorem. Furthermore, for a scatterer excited by a spherical and a plane wave, mixed scattering theorems are derived. Besides, all the derived theorems recover known results, concerning the excitation of a homogeneous scatterer by an exterior dipole. We also analyze numerical implementations of the optical theorem in certain concrete scattering applications. Copyright © 2007 John Wiley & Sons, Ltd.