Vol. 12, No. 4, 2017

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ISSN: 1559-3959
Fully periodic RVEs for technological relevant composites: not worth the effort!

Konrad Schneider, Benjamin Klusemann and Swantje Bargmann

Vol. 12 (2017), No. 4, 471–484
Abstract

The setup of a finite element model for homogenization featuring a fully periodic geometry and a fully periodic mesh topology in combination with a high quality discretization is a cumbersome task and might significantly reduce the overall efficiency in multiscale finite element simulations.

In this work, we examine multiple methodologies of setting up finite element models for homogenization purposes that extenuate these difficulties. Approaches resulting in periodic and nonperiodic representative volume element topologies in the microstructural generation process are introduced. Furthermore, we review and analyze various types of boundary conditions that either enforce periodicity or do not require periodicity of the underlying discretization. Approximate periodic boundary conditions are discussed in detail.

The benchmark study proves that a fully periodic topology and mesh discretization with periodic boundary conditions is not necessary in order to identify effective macroscopic material parameters for technologically relevant composites.

Keywords
periodic boundary conditions, representative volume element, homogenization
Milestones
Received: 25 August 2016
Revised: 28 February 2017
Accepted: 13 March 2017
Published: 22 May 2017
Authors
Konrad Schneider
Institute of Continuum Mechanics and Material Mechanics
Hamburg University of Technology
D-22073 Hamburg
Germany
Benjamin Klusemann
Institute of Product and Process Innovation
Leuphana University of Lüneburg
D-21339 Lüneburg
Germany
Institute of Materials Research
Helmholtz-Zentrum Geesthacht
D-21502 Geesthacht
Germany
Swantje Bargmann
Chair of Solid Mechanics
University of Wuppertal
D-42119 Wuppertal
Germany