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This paper studies the stress concentration around an elliptical hole embedded in an elastic medium under a far-field incident harmonic SH wave. Compared with related existing studies in the literature, the current study particularly incorporates surface elasticity effects in case the size of the hole falls within the micro- or lower-scale. The elliptic coordinate system and the Mathieu functions are introduced to solve the corresponding boundary value problem, and a series-form solution is obtained for the full-field scattering wave function. The dynamic stress concentration around the hole induced by the far-field incident wave is illustrated via a group of numerical examples. It is shown that the surface effect suppresses the fluctuation of the dynamic stress distribution around the hole and reduces significantly the dynamic stress concentration around the hole at the micro- or lower-scale. [ABSTRACT FROM AUTHOR]

Hollow fibers are commonly introduced into flexible thermoelectric materials for certain engineering applications. However, significant stress concentration may be caused in the vicinity of the interface between the fibers and thermoelectric matrix threatening the reliability of the composite structure. In this paper, we study the plane deformation problem of a rigid hollow fiber embedded in a thermoelectric material. By utilizing the complex variable method, the closed‐form solutions for electric, thermal and elastic fields in both of the fiber and the matrix are obtained. The effects of the thermal resistance and geometric parameters of the hollow fiber on the temperature and stress distributions are numerically examined. The results show that the temperature difference (amplitude of variation in temperature in the matrix side around the interface) and the stress field around the interface are proportion to the inner radius of the hollow fiber and the thermal resistance, respectively. Meanwhile, we find that the temperature and the stress distributions are more sensitive to the geometric parameters than to the thermal resistance. The results in this paper may serve as guidelines for design of fibers‐filled thermoelectric structures. [ABSTRACT FROM AUTHOR]

• Analytic algorithm for SH wave scattering near semi-elliptical crater. • The boundary of the crater is endowed with surface elasticity. • DSCF relative to wave frequency, incident angle and crater's aspect ratio. Cratering occurs inevitably on the surface of materials at all scales due to comprehensive factors. The presence of craters may have a significant influence on the mechanical performance of the surface of an elastic body. In this paper, we study the SH wave propagation in an elastic semi-infinite medium whose surface has a semi-elliptical crater. We explore the scattering of the SH wave by the crater when surface elasticity is incorporated in the model of deformation to account for possible small-scale effects of the crater. We obtain a series solution for the scattered wave function by employing the Mathieu functions in the corresponding elliptical coordinate system. We discuss in some numerical examples the dynamic stress concentration around the crater relative to the wave frequency and few geometric parameters. [ABSTRACT FROM AUTHOR]

We analyze the contribution of surface elasticity and electric current density on the thermal stress distribution around a circular nano-hole in a thermoelectric material. Using complex variable methods, we obtain closed-form solutions describing the corresponding thermoelastic fields in the vicinity of the nano-hole. Our results indicate that the effect of surface elasticity is to generate significant normal and shear stresses on the boundary of the hole, allowing for the ability to either suppress or enhance hoop stress depending on the sign of the corresponding surface material constant. In addition, we find that positive hoop stress generated on the boundary by the remote electric current density can be neutralized by the incorporation of positive surface elasticity. In the case of the remaining boundary stress components, both surface elasticity and electric current density are found to enhance normal stress, while the maximum shear stress depends largely on the contribution of surface elasticity. [ABSTRACT FROM AUTHOR]

In the mechanical analysis of a structure/composite with periodic holes/inhomogeneities based on analytic techniques, the holes/inhomogeneities are usually assumed to be circular. In this paper, we develop an efficient method (based on complex variable techniques) to calculate the surface tension-induced stress field in a porous material containing a periodic array of unidirectional holes of arbitrary shape. In this method, we use conformal mapping and Faber series techniques to address a finite representative unit cell (RUC) consisting of a single arbitrarily-shaped hole with a constant surface tension imposed on the hole’s boundary and periodic deformations imposed on the edge of the RUC. Several numerical examples are presented to verify the accuracy of our method and to study the influence of the shape and volume fraction of the periodic holes on the stress concentration in the structure. We show that the maximum hoop stress around periodic holes of some shapes (such as triangle, pentagon or hexagon) may appear exactly at the point(s) of maximum curvature when the hole volume fraction exceeds a certain value. Moreover, when the hole volume fraction falls below about 7%, it is found that the surface tension-induced stress concentration around periodic holes can be treated approximately as that around a single hole with the same hole shape and size in an infinite plane. [ABSTRACT FROM AUTHOR]

We propose an innovative numerical scheme (based on complex variable techniques) for the calculation of the effective properties of a composite containing unidirectional periodic fibers in which we additionally incorporate the separate contribution of the 'interface effect' between the fibers and the surrounding material. The incorporation of interface effect into the model of deformation allows our model to accommodate the general class of nanocomposite materials, a fast growing area of research and our primary focus in this paper. The composite is loaded by a constant normal strain along the direction parallel to the fibers and by a uniform remote loading in the plane perpendicular to the fibers. Our method is based on the analysis of a representative unit cell with periodic boundary conditions imposed on its edge. Several examples are presented to study the influence of the interface and the volume fraction of the fibers on the effective properties of the composite and the interfacial stress field. We show that when the volume fraction falls below roughly 9%, the interfacial stress distribution recovers effectively to that corresponding to a single fiber with the same interface parameters embedded within an infinite matrix. We find also that if the shear modulus of the fibers exceeds approximately two and a half times that of the matrix, the interface effect is negligible in the determination of the effective properties of the corresponding nanocomposites. Finally, we show that the use of traditional effective medium theories may induce significant errors in the determination of transverse effective properties (in the plane perpendicular to the fibers) of the composite, in particular when the fibers are significantly softer than the matrix. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the problem of stress concentration in an infinite plate with an elliptic hole reinforced by a functionally graded layer based on the complex variable method combined with the technique of conformal mapping. With using the method of piece-wise homogeneous layers, the general solution for the functionally graded layer having normal arbitrary elastic properties is derived when the plate is subjected to arbitrary constant loads at infinity, and then numerical results are presented for several special examples. It is found that the existence of the functionally graded layer can influence the stress distribution in the plate, and thus choosing proper variations of the normal elastic properties and proper thicknesses of the layer can effectively reduce the stress concentration around the elliptic hole. [ABSTRACT FROM AUTHOR]

This paper presents a perturbation solution to a two-dimensional problem of two arbitrarily shaped holes within an infinite piezoelectric solid subjected to uniform mechanical and electric loads at infinity. Of particular interest are the stress field and electric field around hole with relation to the distance between the two holes. The shape of each hole is characterized by a truncated mapping which can be regarded as that for an elliptical hole with a perturbation. By using the perturbation method and Faber series, both the complex potentials of the piezoelectric solid and the electric fields inside holes are expressed in a series form with unknown coefficients to be determined by Fourier expansion method. Detailed numerical results are shown for oval, elliptical, triangular and square holes. A basic conclusion is that the hoop stress and electric field strength nearby the point of maximum curvature on the hole׳s boundary increase rapidly with decreasing distance between the point of maximum curvature and the other hole. On the other hand, it is shown that the electric field inside non-elliptical hole is always non-uniform regardless of the distance between the two holes, while that inside elliptical hole tends to be uniform with increasing distance between the two holes. Additionally, if the distance between the two holes is more than four times the hole size, the interaction between the two holes is ignorable and the problem of two holes can be divided into two separate problems of only a single hole. [ABSTRACT FROM AUTHOR]

Abstract: Electro-elastic fields in an infinite matrix with N coated-piezoelectric inclusions are studied based on the complex variable method. Based on the assumption that the coated inclusions are completely bounded the matrix which is subjected to remote anti-plane shears and in-plane electric fields, the general solutions for complex potentials are first derived for arbitrary arrays of inclusions. Then, the numerical results are obtained for special cases in which the inclusions are located in different ways. Discussions are made about the influence of the coating thickness, the array type of inclusions and the material properties on the interface stresses and electric displacements in the matrix. It is found that both the array types of inclusions and the Young’s modulus of the three-phase material system have remarkable effects on stresses, but not on electric displacements, while the piezoelectric constants of the coating and its thickness have significant effects on electric displacements, but not on stresses. [Copyright &y& Elsevier]

Abstract: In this paper the two-dimensional problem of a bolt loaded-hole in an infinite piezoelectric laminate is considered in terms of the complex variable method. Firstly, an explicit form Green function for a generalized point load acted at an arbitrary point outside the hole is derived. Secondly, the Green function for a generalized point load acted at the rim of the hole, as a special case, is obtained, and then a general solution for the case of arbitrarily distributed mechanical and electric loading on the hole surface is presented based on the superposition principle. In general, the solution is in the form of series, but its novel feature is that the coefficients involved in the solution can be easily written out once the distributed loading is specified. Finally, several examples useful for engineering are given. [Copyright &y& Elsevier]

Thermoelectricity is a class of material possessing the ability of interconverting heat and electricity. For the sake of high conversion efficiency, inclusions/fibers are usually introduced into thermoelectric materials. However, the discontinuity of material property and geometry brought by inclusions/fibers might result in severe stress concentration and thus greatly affect the mechanical properties of thermoelectric material in its engineering service. This paper introduces a nonlinear coupled thermal–electrical–mechanical formulation for the plane problem of a circular inhomogeneity embedded in a thermoelectric medium under a combined uniform electric current density and energy flux. A special attention is directed towards the induced thermal stress field which has often neglected in the literature. Using methods based on Cauchy integrals, the complex potentials of the electric field, temperature field and associated stress field are derived explicitly in both the inhomogeneity and the surrounding matrix. The analysis shows that the electrically and thermally induced stress has a linear relationship with the energy flux applied at infinity, but has a nonlinear relationship with the remote electric current density. Numerical simulations are also performed to examine how the inhomogeneity influences the electrically induced thermal stress concentration on the interface. The presented results can be directly used for reliability consideration in design and optimization of thermoelectric composites with circular fibers/inclusions. [ABSTRACT FROM AUTHOR]

• Thermoelastic inclusion problem with nonlinear electric current effects has been solved using complex function theory. • The shape, bluntness and orientation of the inclusion significantly affect the stress concentration around it. • Stress concentration around the quasi-hexagonal inclusion can be lower than that around a circular inclusion. The presence of inclusions in metal-based composites subjected to an electric current or a heat flux induces thermal stresses. Inclusion geometry is one of the important parameters in the stress distribution. In this study, the plane problem of an arbitrarily-shaped inclusion embedded in an infinite conductive medium is investigated based on the complex variable method. The shape of the inclusion is defined approximately by a polynomial conformal mapping function. Faber series and Fourier expansion techniques are used to solve the corresponding boundary value problems. The obtained results show that the shape, bluntness and rotation angle of the inclusion have a significant effect on the stress concentration around the inclusion induced by the far-field electric current. In addition, for the considered inclusion-matrix system under given electric loading, a lower amount of the Von Mises stress concentration than that around a circular inclusion could be achieved by appropriate selection of the inclusion shape and orientation. [ABSTRACT FROM AUTHOR]

We use conformal mapping techniques to derive a semi-analytical solution to the problem of a (straight) screw dislocation embedded in a thin solid film. The surfaces of the film are assumed to incorporate surface effects which result in deformation-dependent tractions imposed on the surfaces of the film. A number of examples are used to illustrate the stress distribution in the film and the image force acting on the dislocation. We show that in the absence of surface effects significant errors are induced in the determination of both the stress field in the film and the mobility of the dislocation, in particular as the dislocation approaches each of the film's surfaces or as the film becomes thinner. In fact, we demonstrate that the incorporation of surface effects with either positive or negative (surface) shear modulus can either relieve or intensify the stress concentration on the surfaces of the film. We find also that the dislocation tends to move towards a surface which possesses a smaller surface shear modulus and a smaller distance to the dislocation. Moreover, we show that when the thickness of the film exceeds ten times the (smaller) distance between the film's surfaces and the dislocation, the film can be treated essentially as a half-space without inducing large errors in the determination of the stress field in the film and the image force imposed on the dislocation. [ABSTRACT FROM AUTHOR]

We examine the surface tension-induced stress concentration around an elliptical hole inside an anisotropic half-plane with traction-free surface. Using conformal mapping techniques, the corresponding complex potential in the half-plane is expressed in a series whose unknown coefficients are determined numerically. Our results indicate that the maximum hoop stress around the hole (which appears in the vicinity of the point of maximum curvature) increases rapidly with decreasing distance between the hole and the free surface. In particular, for an elliptical or even circular hole in an anisotropic half-plane we find that, with decreasing distance between the hole and the free surface, the hoop stress can switch from compressive to tensile at certain points on the hole's boundary and from tensile to compressive at others. This phenomenon is absent in the case of an elliptical or even circular hole in the corresponding case of an isotropic half-plane. [ABSTRACT FROM AUTHOR]