Problems of the concentration of elastic stresses near defects in spherically multilayered media

A spherically multilayered medium, whose elastic parameters change abruptly on the spherical surfaces, with defects in the form of cracks or thin rigid inclusions, is considered. The method of solving problems of the stress concentration near such defects is based on the introduction of linear combinations of the displacements and stresses as the fundamental unknowns. This enables the difficulties related to the presence of an arbitrary number of layers to be effectively overcome. The method is described initially for an unbounded elastic medium and defects of spherical form, situated on the surfaces where the elastic parameters change (interphase defects) and a way of extending this to the case of an elastic medium of finite dimensions, defects of other forms and not situated on these surfaces, is indicated. The method is described in detail as it applies to the case of a two-layer medium with an interphase crack when a torsion centre at the origin of coordinates acts on the medium. The problem is reduced to an integral equation, an effective method of solving it is given, and a formula is obtained for the stress intensity factor.