On the equivalent inclusion method and impotent eigenstrains

The equivalency equations and the nature of the solution are investigated when an inhomogeneity under applied stresses is simulated by an inclusion with eigenstrains. The equivalency equations by which the equivalent eigenstrain is obtained becomes singular when the inhomogeneity is void and the applied stress has a form of polynomials of coordinates of degree one. The solutions of the system of the equivalency equations are not uniquely determined. Explicit expressions are given for the impotent eigenstrains which do not generate any stress field throughout a material.This research was supported by the U.S. Army Research Office under Grant No. DAAG 29-77-G-0042 to Northwestern University.On leave of absence of Meiji University, Tokyo.