Comparison of current methods for implementing periodic boundary conditions in multi-scale homogenisation

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dc.contributor.authorHenyš, Petr
dc.contributor.authorČapek, Lukáš
dc.contributor.authorBřezina, Jan
dc.date.accessioned2019-10-29T07:44:43Z
dc.date.available2019-10-29T07:44:43Z
dc.date.issued2019
dc.description.abstractCorrectly 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.cs
dc.format.extent13 strancs
dc.identifier.WebofScienceResearcherIDF-3530-2015 Březina, Jan
dc.identifier.doi10.1016/j.euromechsol.2019.103825
dc.identifier.issn9977538
dc.identifier.orcid0000-0002-8700-0163 Henyš, Petr
dc.identifier.orcid0000-0003-3950-0646 Čapek, Lukáš
dc.identifier.orcid0000-0002-2246-7344 Březina, Jan
dc.identifier.urihttps://dspace.tul.cz/handle/15240/154066
dc.identifier.urihttps://www.sciencedirect.com/science/article/pii/S0997753818308453
dc.language.isocscs
dc.publisherElsevier Ltd
dc.relation.ispartofEuropean Journal of Mechanics, A/Solids
dc.subjectFinite elementcs
dc.subjectHeterogeneous materialcs
dc.subjectMulti-scale homogenisationcs
dc.subjectNitsche's methodcs
dc.subjectPeriodic boundary conditionscs
dc.subjectPolynomial interpolationcs
dc.titleComparison of current methods for implementing periodic boundary conditions in multi-scale homogenisationcs
local.article.number103825
local.identifier.publikace7252
local.relation.volume78
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