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A circular inclusion in a finite domain I. The Dirichlet-Eshelby problem

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This is the first paper in a series concerned with the precise characterization of the elastic fields due to inclusions embedded in a finite elastic medium. A novel solution procedure has been developed to systematically solve a type of Fredholm integral equations based on symmetry, self-similarity, and invariant group arguments. In this paper, we consider a two-dimensional (2D) circular inclusion within a finite, circular representative volume element (RVE). The RVE is considered isotropic, linear elastic and is subjected to a displacement (Dirichlet) boundary condition. Starting from the 2D plane strain Navier equation and by using our new solution technique, we obtain the exact disturbance displacement and strain fields due to a prescribed constant eigenstrain field within the inclusion. The solution is characterized by the so-called Dirichlet-Eshelby tensor, which is provided in closed form for both the exterior and interior region of the inclusion. Some immediate applications of the Dirichlet-Eshelby tensor are discussed briefly.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of California, Berkeley, CA, 94720, U.S.A

    S. Li, R. Sauer & G. Wang

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  1. S. Li
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  2. R. Sauer
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  3. G. Wang
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Correspondence to S. Li.

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Li, S., Sauer, R. & Wang, G. A circular inclusion in a finite domain I. The Dirichlet-Eshelby problem. Acta Mechanica 179, 67–90 (2005). https://doi.org/10.1007/s00707-005-0234-2

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  • DOI: https://doi.org/10.1007/s00707-005-0234-2

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