Aspects of implementing constant traction boundary conditions in computational homogenization via semi-Dirichlet boundary conditions

Date
2017
Authors
Javili, A.
Saeb, S.
Steinmann, P.
Advisor
Supervisor
Co-Advisor
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Instructor
Source Title
Computational Mechanics
Print ISSN
0178-7675
Electronic ISSN
1432-0924
Publisher
Springer Verlag
Volume
59
Issue
1
Pages
21 - 35
Language
English
Type
Article
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Journal ISSN
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Abstract

In the past decades computational homogenization has proven to be a powerful strategy to compute the overall response of continua. Central to computational homogenization is the Hill–Mandel condition. The Hill–Mandel condition is fulfilled via imposing displacement boundary conditions (DBC), periodic boundary conditions (PBC) or traction boundary conditions (TBC) collectively referred to as canonical boundary conditions. While DBC and PBC are widely implemented, TBC remains poorly understood, with a few exceptions. The main issue with TBC is the singularity of the stiffness matrix due to rigid body motions. The objective of this manuscript is to propose a generic strategy to implement TBC in the context of computational homogenization at finite strains. To eliminate rigid body motions, we introduce the concept of semi-Dirichlet boundary conditions. Semi-Dirichlet boundary conditions are non-homogeneous Dirichlet-type constraints that simultaneously satisfy the Neumann-type conditions. A key feature of the proposed methodology is its applicability for both strain-driven as well as stress-driven homogenization. The performance of the proposed scheme is demonstrated via a series of numerical examples. © 2016, Springer-Verlag Berlin Heidelberg.

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Keywords
Computational homogenization, Constant traction boundary conditions, Finite strains, Semi-Dirichlet boundary conditions
Citation
Published Version (Please cite this version)