Antiplane study on confocally elliptical inhomogeneity problem using an alternating technique

2010

Arch Appl Mech

This paper investigated the interaction between an edge dislocation and a nonuniformly coated circular inclusion. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with alternating technique, the solutions to plane elasticity problems for three dissimilar media are derived explicitly in a series form. For a limiting case when the thickness of the interphase layer is uniform, the derived analytical solutions of this paper are reduced to exactly the same results available in the literature. The image force acting on the dislocation is then determined by using the Peach-Koehler formula. It is found that the combination of material constants and nonuniformity of the interphase thickness will exert a significant influence on the dislocation force.

Section: Introductionmentioning

confidence: 99%

Edge dislocation interacting with a nonuniformly coated circular inclusion

2010

Arch Appl Mech

“…It was concluded that the stresses within a multiphase elliptical inclusion are uniform provided that all interfaces consist of confocal ellipses. A novel efficient procedure to analyze the two-phase confocally elliptical inclusion embedded in an unbounded matrix under antiplane loadings was provided [8].Within the framework of linear piezoelectricity, an effective method was developed and used to derive an analytical solution for the problem of a confocally multicoated elliptical inclusion embedded in an unbounded matrix which is subjected to arbitrary electromechanical loadings [9].…”

Section: Introductionmentioning

confidence: 99%

Solution for a Crack Embedded in Multiply Confocally Elliptical Layers in Antiplane Elasticity

2015

J. mech.

This paper provides a general solution for a crack embedded in multiply confocally elliptical layers in antiplane elasticity. In the problem, the elastic medium is composed of an inclusion, many confocally elliptical layers and the infinite matrix with different elastic properties. In addition, the remote loading is applied at infinity. The complex variable method and the conformal mapping technique are used. On the mapping plane, the complex potentials for the inclusion and many layers are assumed in a particular form with two undetermined coefficients. The continuity conditions for the displacement and traction along the interface between two adjacent layers are formulated and studied. By enforcing those conditions along the interface, the exact relation between two sets of two undetermined coefficients in the complex potentials for j-th layer and j 1-th layer can be evaluated. From the traction free condition along the crack faces, the correct form of the complex potential for the cracked inclusion is obtained. Finally, many numerical results are provided.

“…The elliptic inclusion problems in antiplane elasticity and plane elasticity are some particular problems in the field of inclusion problem [4][5][6][7][8][9]. For the antiplane problem of an elastic elliptical inclusion with uniform eigenstrains and arbitrary remote loading, a general solution was provided [4].…”

Section: Introductionmentioning

confidence: 99%

Solution and Numerical Analysis for Thermal Elliptic Inclusion in Plane Elasticity

Journal of Thermal Stresses

2015

By using the conformal mapping technique and the continuity conditions along the interface, a general solution and numerical analysis for thermal elliptic inclusion in plane elasticity are presented. In the study, two types of temperature distributions in the inclusion, the constant distribution and the linear distribution, are assumed. In the first case, the strains and stresses in the inclusion remain constant. However, in the second case, the strains and stresses in the inclusion do not stay constant. For a particular case, a numerical example is carried out.