A Mori–Tanaka homogenization scheme for non-linear elasto-viscoplastic heterogeneous materials based on translated fields: An affine extension

Stéphane Berbenni; Laurent Capolungo

doi:10.1016/j.crme.2014.12.003

A Mori–Tanaka homogenization scheme for non-linear elasto-viscoplastic heterogeneous materials based on translated fields: An affine extension

Stéphane Berbenni ¹ ; Laurent Capolungo ²

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

Comptes Rendus. Mécanique, Mechanics of granular and polycrystalline solids, Volume 343 (2015) no. 2, pp. 95-106.

Abstract

A Mori–Tanaka homogenization scheme based on the “translated fields” approach is extended to elasto-viscoplastic composites with non-linear viscoplasticity described by a first-order “affine”-type linearization. This extension leads to a new theoretical interaction law between mechanical average phase fields and overall ones. This interaction law contains the coupling between elastic- and viscoplastic- mechanical interactions and phase stress histories. In order to study and discuss the validity of the present approach, the results are reported for two-phase composites and are compared to other approaches.

Received: 2014-01-14
Accepted: 2014-04-28
Published online: 2015-01-08

DOI: 10.1016/j.crme.2014.12.003

Keywords: Homogenization, Translated fields, Non-linear composites, Elasto-viscoplastic materials, Mori–Tanaka, Affine formulation

Author's affiliations:

Stéphane Berbenni ¹; Laurent Capolungo ²

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

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     title = {A {Mori{\textendash}Tanaka} homogenization scheme for non-linear elasto-viscoplastic heterogeneous materials based on translated fields: {An} affine extension},
     journal = {Comptes Rendus. M\'ecanique},
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Stéphane Berbenni; Laurent Capolungo. A Mori–Tanaka homogenization scheme for non-linear elasto-viscoplastic heterogeneous materials based on translated fields: An affine extension. Comptes Rendus. Mécanique, Mechanics of granular and polycrystalline solids, Volume 343 (2015) no. 2, pp. 95-106. doi : 10.1016/j.crme.2014.12.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.12.003/

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