Abstract
It is shown, based on properties of analytic functions, that for inclusions of constant eigenstrain and eigenstress that the shape of the inclusion is restricted and any part of a plane (i.e. polyhedral inclusion) is prohibited.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. Bers, F. John, and M. Schechter, Partial Differential Equations, Interscience, New York (1964), p. 136.
J.D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. Roy. Soc. A241, (1957) 376–396.
J.D. Eshelby, Elastic inclusions and inhomogeneities. In I.N. Sneddon and R. Hill (eds), Progress in Solid Mechanics 2, North Holland, Amsterdam, (1961) pp. 89–140.
F. John, Partial Differential Equations, Third Edition, Springer-Verlag, New York (1978) p. 59.
T. Mura, Micromechanics of Defects in Solids, Martinus Nijhoff Publishers, The Hague, Netherlands (1982).
G.J. Rodin, Eshelby's inclusion problem for polygons and polyhedra, J. Mech. Phys. Solids 44 (1996) 1977–1995.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Markenscoff, X. On the Shape of the Eshelby Inclusions. Journal of Elasticity 49, 163–166 (1997). https://doi.org/10.1023/A:1007474108433
Issue Date:
DOI: https://doi.org/10.1023/A:1007474108433