On multiple circular inclusions in plane magnetoelasticity

A general series solution to the magnetoelastic problem of interacting circular inclusions in plane magnetoelasticity is provided in this paper. By the use of complex variable theory and Laurent series expansion method, the general expression of the magnetic and the magnetoelastic complex potentials for the circular inclusion problem is derived. Expanding the definition of the Airy’s stress function of pure elastic field into the magnetoelastic field and applying the superposition method, the general expression then can be reduced to a set of linear algebraic equations and solved in a series form. An approximate closed form solution for the case of two arbitrarily located inclusions is also provided. For illustrating the effect of the pertinent parameters, the numerical results of the interfacial magnetoelastic stresses are displayed in graphic form.     

Stress-strain state of an elastic half-plane with rectangular inclusions

Conclusions As is seen from Fig. 5, elevated stress zones are formed for small distances d<0.2a between the inclusions. In practice there is no mutual influence between the inclusions for distances d>2.5a since the distribution of the stress along the line x₁=0 for d=5a is the same as for the case of a half-plane without inclusions.Kiev University. Translated from Prikladnaya Mekhanika, Vol. 26, No. 5, pp. 56–61, May, 1990.     

Two circular inclusions with inhomogeneously imperfect interfaces in plane elasticity

This paper is concerned with the problem of two circular inclusions with circumferentially inhomogeneously imperfect interfaces embedded in an infinite matrix in plane elastostatics. Infinite series form solutions to this problem are derived by applying complex variable techniques. The numerical results demonstrate that the interface imperfection, interface inhomogeneity, and interaction among neighboring inclusions (fibers) will exert a significant influence on the stresses along the interfaces and average stresses within the inclusions.     

含圆形嵌体弹性平面中径向裂纹问题的超奇异积分方程方法

根据含圆形嵌体平面问题在极坐标下的弹性力学基本解,使用Betti互换定理,在有限部积分意义下将问题归结为两个以裂纹岸位移间断为基本未知量、对于Ⅰ型和Ⅱ型问题相互独立的超奇异积分方程,对含圆形嵌体弹性平面中的径向裂纹问题进行了研究.根据有限部积分原理,建立了问题的数值算法.计算结果表明,嵌体半径、裂纹位置及材料剪切弹性模量等都对裂纹应力强度因子具有较为明显的影响.     

Inclusions in a finite elastic body

Within the framework of 2D or 3D linear elasticity, a general approach based on the superposition principle is proposed to study the problem of a finite elastic body with an arbitrarily shaped and located inclusion. The proposed approach consists in decomposing the initial inclusion problem into the problem of the inclusion embedded in the corresponding infinite body and the auxiliary problem of the finite body subjected to the appropriate boundary loading provided by solving the former problem. Thus, our approach renders it possible to circumvent the difficulty due to the unavailability of the relevant Green function, use various existing solutions for the problem of an inclusion inside an unbounded body and clearly makes appear the finite boundary effects. The general approach is applied and specified in the context of 2D isotropic elasticity. The complex potentials for the problem of an inclusion in an infinite body are given as two boundary integrals, and the boundary integral equation governing the complex potentials for the auxiliary problem is provided. In the important particular situation where a finite body with an arbitrarily shaped and located inclusion is circular, the exact explicit expressions for the complex potentials are derived, leading to those for the strain, stress and Eshelby’s tensor fields inside and outside the inclusion. These results are analytically detailed and numerically illustrated for the cases of a square inclusion placed concentrically, and a circular inclusion located eccentrically, inside a circular body.     

BEM for simulation of a 2D elastic body with randomly distributed circular inclusions

Based on our 2D BEM software THBEM2 which can be applied to the simulation of an elastic body with randomly distributed identical circular holes, a scheme of BEM for the simulation of elastic bodies with randomly distributed circular inclusions is proposed. The numerical examples given show that the boundary element method is more accurate and more effective than the finite element method for such a problem. The scheme presented can also be successfully used to estimate the effective elastic properties of composite materials. Project supported by the National Natural Science Foundation of China (No. 19772025).     

On the load transfer from elastic inclusions to an infinite elastic orthotropic plane with cuts

The present paper deals with the problem of load transfer from elastic inclusions to an infinite elastic orthotropic plane with cuts located on one of the principal orthotropy directions. The constitutive system of equations of this problem is derived under the assumption that the inclusions are in a uniaxial stress state. The obtained system consists of a singular integro-differential equation and a singular integral equation for the jumps of the tangential stresses acting on the inclusion shores and for the derivative of the the cut opening function. The behavior of solutions of the system of constitutive equations at the endpoints of the inclusions and cuts is studied, and the solution of this system is constructed by the numerical-analytic discrete singularity method.     

BOUNDARY INTEGRAL FORMULAS FOR ELASTIC PLANE PROBLEM OF EXTERIOR CIRCULAR DOMAIN

After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.     

Gas‐assisted fluid displacement in a circular tube and a rectangular channel

In this paper the amount of liquid left inside of a circular tube and a rectangular channel when displaced by another immiscible fluid are determined by solving the full creeping‐motion equations. The exact continuity of stress on the free surface is employed with a finite difference method. In order to solve the equations, the steady‐state shape of the interface is guessed and the normal stress boundary condition is dropped. The equations based on a stream function‐vorticity formulation are solved with the aid of elliptic grid generation. The computed results are compared with the experimental results of Taylor (J. Fluid Mech. 1961; 10: 161), the theoretical results of Reinelt and Saffman (SIAM J. Sci. Stat. Comput. 1985; 6: 542) and our experimental data. The computed results are in close agreement with our experimental data and those of previous investigators. Copyright © 2002 John Wiley & Sons, Ltd.     

The symmetry and loading-independency of multiple inclusions enclosing uniform stresses in an infinite elastic plane

The identification of multiple interacting inclusions with uniform internal stresses in an infinite elastic matrix subjected to a uniform remote loading is of fundamental importance in the mechanics and design of particulate composite materials. In anti-plane shear and plane deformations, certain sufficient conditions have been established in the literature which guarantee uniform internal stresses inside multiple interacting inclusions displaying various symmetries when the matrix is subjected ...     

Axisymmetric scattering of plane stationary waves on absolutely rigid inclusions in an elastic medium

International Applied Mechanics -     

Initiation of localized plane deformations at a circular cavity in an infinite compressible nonlinearly elastic medium

This investigation is concerned with the plane strain deformation of an infinite slab, containing a circular cavity, within the theory of finite elastostatics for a particular homogeneous isotropic compressible material, the so-called Blatz-Ko material. The body is subjected to uniform pressure, either internal or external. Exact closed-form solutions for the axisymmetric deformation and stress fields are obtained. In the case of internal pressure, it is found that the applied pressure may not exceed a certain maximum value p _max. At a value of pressure p _e (<p _max), the governing equations lose ellipticity at the cavity wall. For greater values of pressure this solution remains smooth, though involving both elliptic and non-elliptic regions. Non-existence of axisymmetric solutions with discontinuous strain fields is established. The possibility of bifurication into a surface mode is considered and it is shown that this occurs at a value of pressure slightly smaller than p _e. Such surface wrinkling leads to a periodic distribution of points of stress concentration, from which shear bands may initiate.This work was supported by the U.S. Army Research Office under Grant DAAG29-83-K-0145 (R.A. & C.O.H.) and by the U.S. National Science Foundation under Grant MEA 78-26071 (C.O.H.).     

Motion of a circular cylinder in a rectangular channel

When bodies move in fluids, the parameters of their motion depend strongly on the interaction of the bodies with the surrounding fluid [1, 2]. The present paper is devoted to determination of the hydrodynamic forces that act on a cylinder moving in an infinite rectangular channel in an ideal incompressible fluid that is at rest.