THE CORRESPONDENCE BETWEEN CAVITIES AND RIGID INCLUSIONS IN 3-DIMENSIONAL ELASTICITY AND THE COSSERAT SPECTRUM

The Dundurs' correspondence in plane elasticity between the stress fie lds of cavities and rigid inclusions in the limit as lambda + 2 mu --> 0 (or k --> -1) holds true also in three-dimensional elasticity, but only for dilatation constant or linear function of position. In genera l, in the limit lambda + 2 mu --> 0, the normal traction between rigid inclusion and matrix vanishes, and the shear traction is T-n = 2 mu(O mega-omega)\(k=-1) xn. An example of a rigid spherical inclusion in a sphere under pressure is presented. A proof for the existence of the l imit as lambda + 2 mu --> 0 (when ellipticity fails) is also presented based on the properties of the Cosserat spectrum.