Abstract
The problem of an ellipsoidal inhomogeneity embedded in an infinitely extended elastic medium with sliding interfaces is investigated. An exact solution is presented for such an inhomogeneous system that is subject to remote uniform shearing stress. Both the elastic inclusion and matrix are considered isotropic with a separate elastic modulus. Based on Lur’e’s approach to solving ellipsoidal cavity problems through Lamé functions, several harmonic functions are introduced for Papkovich-Neuber displacement potentials. The displacement fields inside and outside the ellipsoidal inclusion are obtained explicitly, and the stress field in the whole domain is consequently determined.
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Eshelby J D. The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc Roy Soc A-Math Phys, 1957, 241: 376–396
Eshelby J D. Elastic Inclusions and Inhomogeneities. 2nd ed. Amsterdam: North Holland, 1961
Walpole L J. The elastic field of an inclusion in an anisotropic medium. Proc Phil Soc A, 1967, 300: 270–289
Mura T. Micromechanics of Defects in Solids. Dordrecht: Martinus Nijhoff Publishers, 1987
Nemat-Nasser S, Hori M. Micromechanics: Overall Properties of Heterogeneous Material. New York: Elsevier, 1993
Wang M Z, Xu B X. The arithmetic mean theorem of Eshelby tensor for exterior points outside the rotational symmetrical inclusion. J Appl Mech-T ASME, 2006, 73: 672–678
Zheng Q, Zhao Z, Du D. Irreducible structure, symmetry and average of Eshelby’s tensor fields in isotropic elasticity. J Mech Phys Solids, 2006, 54: 368–383
Mura T, Furuhashi R. The elastic inclusion with sliding interface. J Appl Mech-T ASME, 1984, 51: 308–310
Mura T. Mechanics of Defects in Solids. Dordrecht: Martinus Nijhoff Publishers, 1987
Jasiuk I, Tsuchida E, Mura T. The sliding inclusion under shear. Int J Solids Struct, 1987, 23: 1373–1385
Zhong Z, Meguid S A. On the eigenstrain problem of a spherical inclusion with an imperfectly bonded interface. J Appl Mech-T ASME, 1996, 63: 877–883
Zhong Z, Meguid S A. On the elastic field of a spherical inhomogeneity with an imperfectly bonded interface. J Elast, 1997, 46: 91–113
Wang M Z, Xu B X, Gao C F. Recent general solutions in linear elasticity and their applications. Appl Mech Rev, 2008, 61: 030803
Lur’e A I. Three-dimensional Problems of the Theory of Elasticity. New York: Interscience, 1964
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Zhao, Y., Gao, Y. & Wang, M. Inhomogeneity problem with a sliding interface under remote shearing stress. Sci. China Phys. Mech. Astron. 55, 2122–2127 (2012). https://doi.org/10.1007/s11433-012-4902-7
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DOI: https://doi.org/10.1007/s11433-012-4902-7