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A spherical Eshelby inclusion with a Steigmann-Ogden interface in a finite domain
Received date: 2026-01-06
Revised date: 2026-04-21
Online published: 2026-06-30
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We derive closed-form solutions to the three-dimensional Eshelby’s problem of a spherical Eshelby inclusion undergoing uniform deviatoric eigenstrains concentrically embedded in an isotropic elastic finite spherical domain with a traction-free or rigidly clamped boundary. The interface between the inclusion and its surrounding domain is assumed to be of Steigmann-Ogden type. Our solutions indicate that the stresses and strains within the spherical inclusion are generally nonuniform because of the effects of the finite spherical domain and the Steigmann-Ogden imperfect interface. The internal elastic field of stresses and strains is uniform within the spherical inclusion when a condition that relates the single interface parameter to the geometric parameter and Poisson’s ratio of the finite domain is satisfied. When the spherical edge is rigidly clamped, a Gurtin-Murdoch interface is found to be sufficient to achieve this interior uniformity property. In contrast, when the spherical edge is traction-free, a Steigmann-Ogden interface with nonzero and positive bending stiffness parameters must be used to achieve the interior uniformity property.
Xu WANG , P. SCHIAVONE . A spherical Eshelby inclusion with a Steigmann-Ogden interface in a finite domain[J]. Applied Mathematics and Mechanics, 2026 , 47(7) : 1569 -1580 . DOI: 10.1007/s10483-026-3403-9
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