The Eshelby tensor |
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| Authors: | I.Yu. Tsvelodub |
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| Affiliation: | 1. Laboratoire d''étude des microstructures et de mécanique des matériaux, UMR CNRS 7239, Université de Lorraine, île du Saulcy, 57045 Metz, France;2. George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA;1. Mechanics and Aerospace Design Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON M5S 3G8, Canada;2. Texas A&M University at Qatar, Mechanical Engineering Program, Engineering Building, P.O. Box 23874, Education City, Doha, Qatar;1. Université Tunis El Manar, Laboratoire de Génie Civil (LGC), Ecole Nationale d’Ingénieurs de Tunis, BP 37, Le Belvédère, 1002 Tunis, Tunisia;2. Université catholique de Louvain (UCL), IMMC, Bâtiment Euler, 4 Avenue G. Lemaître, B-1348 Louvain-La-Neuve, Belgium;1. Department of Environmental Informatics, Helmholtz Centre for Environmental Research – UFZ, Leipzig, Germany;2. Applied Environmental Systems Analysis, Technische Universität Dresden, Dresden, Germany;3. Department of Mechanical and Manufacturing Engineering, School of Engineering, Trinity College Dublin, College Green, Dublin, Ireland |
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| Abstract: | The problem of the existence of a tensor that is inverse to the well-known Eshelby tensor, which connects the free homogeneous and hindered strains of an ellipsoidal elastic inclusion undergoing transformation, is investigated. It is shown that this tensor exists for inclusions in the form of oblate and prolate spheroids in isotropic elastic space. Certain applications are considered, in particular problems of determining the stresses in ellipsoidal rigid and rigid plastic inclusions. |
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