Validation of the tangent formulation for the solution of the non-linear Eshelby inclusion problem期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Validation of the tangent formulation for the solution of the non-linear Eshelby inclusion problem

Institution:	1. Ufa State Aviation Technical University, Ufa 450008, Russia;2. Laboratory for Mechanics of Bulk Nanomaterials, Saint Petersburg State University, Saint Petersburg 198504, Russia;3. School of Materials Science and Engineering, Changzhou University, Changzhou 213164, PR China;4. Sino-Russian Joint Laboratory of Functional Nanostructured Materials, Changzhou University, Changzhou 213164, PR China;1. Storengy, Immeuble Djinn, 12 rue Raoul Nordling, Bois-Colombes Cedex, 92274 France;2. ENPC, Institut Navier, 6 & 8 avenue Blaise Pascal, Marne-la-Vallée, 77455 France;1. Materials innovation institute (M2i), P.O. Box 5008, 2600 GA Delft, The Netherlands;2. Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;3. Philips Research Laboratories, High Tech Campus 4, Eindhoven, The Netherlands

Abstract:	An extension of the Eshelby problem for non-linear viscous materials is considered. An ellipsoidal heterogeneity is embedded in an infinite matrix. The material properties are assumed to be uniform within the ellipsoid and in the matrix. The problem of determining the average strain rate in the ellipsoid in terms of the overall applied strain rate is solved in an approximate way. The method is based on the non-incremental tangent formulation of the non-linear matrix behavior Acta Metall. 35 (1987) 2983]. In the present work this approximate solution is verified with a good agreement by comparing to finite element calculations for various inclusion shapes and loading conditions.

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