Axisymmetric Inclusion in a Half Space

Abstract

An alternate method of approach for solving the axisymmetric elastic fields in the half space with an isotropic spheriodal inclusion is proposed. This new approach involves the application of the Hankel transformation method for the solution of prismatic dislocation loops and Eshelby’s solution for ellipsoidal inclusions. Existing solutions by other methods for the inclusion with pure dilatational misfit in a half space are shown to be special cases of the present, more general solution.

Thermoelastic stresses in bimaterials

“…The usual suffix notation has been used (a repeated suffix indicates summation over the values 1, 2, 3, and suffixes preceded by a comma denote differentiation with respect to the Cartesian coordinates corresponding to those Downloaded by [University of California, San Diego] at 12:32 29 June 2016 suffixes). Detailed expression for the Galerkin vectors for these nuclei of strain have been given by Yu and Sanday (1991b). The displacement dui in the solid due to du' at point x' is for point x in region I or inside the infinitesimal inclusion, and…”

“…Mindlin and Cheng's method was used by Bratt, Bergman and Solomon (1985) to study the thennoelastic stress in the oceanic lithosphere with the assumption that the oceanic lithosphere can be represented as a uniform elastic half-space. In a very recent paper, Yu and Sanday (1990), using the Hankel transformation method, presented a solution to the problem of a half-space in which an axisymmetric ellipsoidal inclusion undergoes a homogeneous tensile eigenstrain. Their problem is equivalent to the thermal stress problem of a uniformly heated or cooled ellipsoidal inclusion with orthotropic coefficient of linear expansion.…”

The strain energy and shape evolution of hydrides precipitated at free surfaces of metals

“…It was applied for cylindrical and rectangular "wires" [21]. (d) Application of the Hankel transform and superposition [22]. Recently a Green function for anisotropic half-space was devised [23].…”

“…Homogeneous systems can be solved analytically [15][16][17][18][19][20][21][22] but analytic solutions for inhomogeneous and anisotropic problems near a free surface become intractable. Numerical methods, in particular the Finite Element Method (FEM) enable the solution of such mechanical problems with complicated material behavior and boundary conditions.…”

The elastic field induced by a hemispherical inclusion in the half-space

“…Numerical results are obtained stress field. An alternate method for solvaxisymmetric elastic fields in the half-space isotropic spheroidal inclusion was proposed by Sanday [9]. In their study, Eshelby's method ellipsoidal inclusion and the Hankel trans- formation method for the prismatic loop were used.…”