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

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• 作者：A. Javili ; S. Saeb ; P. Steinmann
• 关键词：Computational homogenization ; Semi ; Dirichlet boundary conditions ; Constant traction boundary conditions ; Finite strains
• 刊名：Computational Mechanics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：59
• 期：1
• 页码：21-35
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics; Computational Science and Engineering; Classical and Continuum Physics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0924
• 卷排序：59

文摘

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.