On a point defect inside an idealized elastic sphere

Abstract

This paper presents a method of solution for the displacement, stress, and strain due to a point defect located inside a sphere. The solution is represented by a Love stress function in spherical coordinates, which is biharmonic in character. Two axisymmetric types of the point defect are considered. One is treated as a center of dilatation and the other as a double force without moment, or a doublet, oriented axisymmetrically. The Love stress function for the point defect in an infinite solid is specified in each case by a single biharmonic function. The residual tractions on the surface of the sphere left by this function are annulled by superposing two series of biharmonic functions. When the Love stress function is determined, the displacement, stress, and strain can be derived straightforwardly.