Locally periodic unfolding method and two-scale convergence on surfaces of locally periodic microstructures

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Abstract

In this paper we generalize the periodic unfolding method and the notion of two-scale convergence on surfaces of periodic microstructures to locally-periodic situations. The methods that we introduce allow us to consider a wide range of non-periodic microstructures, especially to derive macroscopic equations for problems posed in domains with perforations distributed non-periodically. Using the methods of locally periodic two-scale convergence (l-t-s) on oscillating surfaces and the locally periodic (l-p) boundary unfolding operator, we are able to analyze differential equations defined on boundaries of non-periodic microstructures and consider non-homogeneous Neumann conditions on the boundaries of perforations, distributed non-periodically.
Original languageEnglish
Pages (from-to)1061-1105
Number of pages45
JournalMultiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
Volume13
Issue number3
Early online date30 Sep 2015
DOIs
Publication statusPublished - 2015

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