Abstract
AbstractNew analytical solutions are derived for Eshelby's problem of an inclusion of arbitrary shape undergoing uniform in‐plane eigenstrains in a plane or in one of two bonded half‐planes. The simply‐connected domain occupied by the inclusion is described by a conformal mapping function that maps the interior of the inclusion onto the interior of the unit circle in the image plane. Elementary expressions of the elastic fields in the exterior of the inclusion and the mean stress inside the thermal inclusion are obtained. Typical examples of epitrochoidal, Booth's lemniscate, hypotrochoidal and generalized Booth's lemniscate thermal inclusions are presented to demonstrate the new solutions.
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Schedule a callMore From: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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