On the Dundurs Correspondence Between Cavities and Rigid Inclusions

Abstract

In plane elasticity the solutions of the stress field of rigid inclusion problems yield the solutions of cavity problems loaded by uniform shear tractions σ = 2μ (Ω − ω0 ) |κ = −1 where Ω is the rotation of the inclusion and ω0 the rotation of the material (evaluated at κ = −1, κ being the Kolosov constant). It is proved that if the limit of the stress field for the inclusion problem exists at κ = −1, then it corresponds to a constant rotation field.