A spherical cavity in a micropolar elastic medium and related problems

Abstract

The problem of a spherical cavity in an infinite, linear, isotrofic, micropolar elastic medium is considered. The spectral displacement and stress fields are obtained when arbitrary tractions and couples are prescribed over the surface of the cavity. It is found that, as in the elastic case, the original problem splits into two independent problems corresponding to spheroidal and toroidal motions, respectively. In the case of purely radial static or dynamic displacements, there is no microrotation. The solutions of such micropolar elastic problems can be obtained from the corresponding elastic solutions on replacing μ by μ + (½)x. This correspondence principle is used to perive the micropolar elastic solutions of several problems involving radial displacements only.