Abstract
The relationship between Eshelby’s tensor and ellipsoidal cavity problems is established and discussed. With this connection, explicit expressions of Eshelby’s tensor are derived for orthotropic materials under plane strain condition and under anti-plane condition separately. Comparisons are made with an earlier form of Eshelby’s tensor, and components that were not previously published are explicitly given. As an application of the newly derived Eshelby’s tensor, elliptic inclusion problems with purely dilatational eigenstrains in orthotropic materials are solved. Stress distributions in materials of different symmetric classes are studied and discussed.
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