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Computational homogenization of materials with small deformation to determine configurational forces

Khalaquzzaman, Md. and Xu, Bai-Xiang and Müller, Ralf (2012):
Computational homogenization of materials with small deformation to determine configurational forces.
In: Proc. Appl. Math. Mech., Wiley-VCH Verlag GmbH & Co. KGaA, pp. 423-424, 12, (1), ISSN 16177061,
[Online-Edition: http://dx.doi.org/10.1002/pamm.201210200],
[Article]

Abstract

n this work the mechanical boundary condition for the micro problem in a two-scaled homogenization using a FE2 approach is discussed. The strain tensor is often used in the literature for small deformation problem to determine the boundary conditions for the boundary value problem on the micro level. This strain tensor based boundary condition gives consistent homogenized mechanical quantities, e.g. stress tensor and elasticity tensor, but the present work points out that it leads to unphysical homogenized configurational forces. Instead, we propose a displacement gradient based boundary condition for the micro problem. Results show that the displacement gradient based boundary condition can give not only the consistent homogenized mechanical quantities but also the appropriate homogenized configurational forces. The interpretation of the displacement gradient based boundary condition is discussed.

Item Type: Article
Erschienen: 2012
Creators: Khalaquzzaman, Md. and Xu, Bai-Xiang and Müller, Ralf
Title: Computational homogenization of materials with small deformation to determine configurational forces
Language: English
Abstract:

n this work the mechanical boundary condition for the micro problem in a two-scaled homogenization using a FE2 approach is discussed. The strain tensor is often used in the literature for small deformation problem to determine the boundary conditions for the boundary value problem on the micro level. This strain tensor based boundary condition gives consistent homogenized mechanical quantities, e.g. stress tensor and elasticity tensor, but the present work points out that it leads to unphysical homogenized configurational forces. Instead, we propose a displacement gradient based boundary condition for the micro problem. Results show that the displacement gradient based boundary condition can give not only the consistent homogenized mechanical quantities but also the appropriate homogenized configurational forces. The interpretation of the displacement gradient based boundary condition is discussed.

Journal or Publication Title: Proc. Appl. Math. Mech.
Volume: 12
Number: 1
Publisher: Wiley-VCH Verlag GmbH & Co. KGaA
Divisions: 11 Department of Materials and Earth Sciences
11 Department of Materials and Earth Sciences > Material Science
11 Department of Materials and Earth Sciences > Material Science > Mechanics of functional Materials
Zentrale Einrichtungen
Exzellenzinitiative
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
Exzellenzinitiative > Graduate Schools
Date Deposited: 18 Apr 2013 07:35
Official URL: http://dx.doi.org/10.1002/pamm.201210200
Identification Number: doi:10.1002/pamm.201210200
Funders: The authors acknowledge financial support of German Research Foundation (DFG) in the framework of Graduate Program GRK-814 and the Center for Mathematical and Computational Modelling (CM) 2 at TU Kaiserslautern
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