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Implementation of periodic boundary conditions for loading of mechanical metamaterials and other complex geometric microstructures using finite element analysis

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Abstract

The implementation of periodic boundary conditions (PBCs) is one of the most important and difficult steps in the computational analysis of structures and materials. This is especially true in cases such as mechanical metamaterials which typically possess intricate geometries and designs which makes finding and implementing the correct PBCs a difficult challenge. In this work, we analyze one of the most common PBCs implementation technique, as well as implement and validate an alternative generic method which is suitable to simulate any possible 2D microstructural geometry with a quadrilateral unit cell regardless of symmetry and mode of deformation. A detailed schematic of how both these methods can be employed to study 3D systems is also presented.

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Acknowledgements

K.K.D. acknowledges the financial support from the program of the Polish Minister of Science and Higher Education under the name “Regional Initiative of Excellence” in 2019–2022, project no. 003/RID/2018/19, funding amount 11 936 596.10 PLN.

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Authors and Affiliations

  1. Metamaterials Unit, Faculty of Science, University of Malta, MSD 2080, Msida, Malta

    Luke Mizzi, Daphne Attard, Ruben Gatt, Krzysztof K. Dudek, Brian Ellul & Joseph N. Grima

  2. Institute of Physics, University of Zielona Gora, ul. Szafrana 4a, 65-069, Zielona Gora, Poland

    Krzysztof K. Dudek

  3. Department of Chemistry, Faculty of Science, University of Malta, MSD 2080, Msida, Malta

    Joseph N. Grima

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  1. Luke Mizzi
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Mizzi, L., Attard, D., Gatt, R. et al. Implementation of periodic boundary conditions for loading of mechanical metamaterials and other complex geometric microstructures using finite element analysis. Engineering with Computers 37, 1765–1779 (2021). https://doi.org/10.1007/s00366-019-00910-1

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