A note on the slipping inclusion
The author proves the converse of Mura-Furuhashi's statement [\textit{T. Mura} and \textit{R. Furuhashi}, J. Appl. Mech. 51, 308-310 (1984; Zbl 0544.73018)] that a slipping ellipsoidal inclusion, if not degenerated, having a shear eigenstrain parallel to the axes of inclusion, produces no stress in the matrix or inclusion. According to the author, in the two- dimensional case, the converse of the above theorem is: if there exists a nonzero constant eigenstrain which produces a zero stress field in the matrix, the inclusion is a nondegenerate ellipse. For the three- dimensional case, the author shows that, as far as we concern the same matrix-inclusion system as Mura-Furuhashi's, there exists a uniform nonzero remote stress field which produces no stress in the inclusion.
slipping ellipsoidal inclusion of no degeneracy
scientific article; zbMATH DE number 4174415