Inclusions and inhomogeneities under stress

Abstract

Some general theorems, new and old, concerning the behaviour of elastic inclusions and inhomogeneities in bodies without or with external stress, are assembled. The principal new result is that arbitrary external tractions cannot influence the shape of an inclusion, because the elastic held of the external tractions passes unperturbed through the inclusion, and the work done by the external forces is independent of the shape of the inclusion. The terms in the energy quadratic in the external tractions are unaffected by the presence of the inclusion, and by Colonnetti's theorem the total elastic energy contains no cross terms between internal and external stresses.