Elastic strain energy due to deviatoric eigenstrains in an inclusion having symmetric shape

An inclusion having purely dilatational eigenstrains in an infinitely extended isotropic material causes an elastic strain energy that is independent of its shape. The present study analyses the elastic strain energy caused by an inclusion with purely deviatoric eigenstrains using simple calculations. It is found that the elastic strain energy due to certain types of purely deviatoric eigenstrains is also independent of the inclusion shape provided that the shape satisfies a certain symmetry. This holds even for geometrically complicated inclusion shapes.