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.
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