Comparison of current methods for implementing periodic boundary conditions in multi-scale homogenisation
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Date
2019
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier Ltd
Abstract
Correctly representing the micro-scale model boundaries is fundamental to the performance and accuracy of multi-scale homogenisation. Although enforcing periodic boundary conditions is known to lead to more effective property approximation in comparison with that achieved with kinematic/uniform force boundary conditions, implementing them imposes restrictions on the mesh generation process and makes the process of solving the underlying variational problem more complicated. This study reviews the current implementation methods, which employ meshless and finite element approaches to maintain field periodicity. Finally, we propose a new method based on Nitsche's weak formulation and compare it with other state-of-the-art techniques. The results of several benchmarks demonstrate that all tested methods are highly robust and accurate, with minor method-specific issues.
Description
Subject(s)
Finite element, Heterogeneous material, Multi-scale homogenisation, Nitsche's method, Periodic boundary conditions, Polynomial interpolation
Citation
ISSN
9977538