Periodic homogenization in the context of structured deformations-Reference-Cited by-同舟云学术

Periodic homogenization in the context of structured deformations

Published:2022-07-19 Issue:4 Volume:73 Page:
ISSN:0044-2275
Container-title:Zeitschrift für angewandte Mathematik und Physik
language:en
Short-container-title:Z. Angew. Math. Phys.

Author:

Amar Micol^ORCID,Matias José^ORCID,Morandotti Marco^ORCID,Zappale Elvira^ORCID

Abstract

AbstractAn energy for first-order structured deformations in the context of periodic homogenization is obtained. This energy, defined in principle by relaxation of an initial energy of integral-type featuring contributions of bulk and interfacial terms, is proved to possess an integral representation in terms of relaxed bulk and interfacial energy densities. These energy densities, in turn, are obtained via asymptotic cell formulae defined by suitably averaging, over larger and larger cubes, the bulk and surface contributions of the initial energy. The integral representation theorem, the main result of this paper, is obtained by mixing blow-up techniques, typical in the context of structured deformations, with the averaging process underlying the theory of homogenization.

Funder

Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni

Ministero dell’Istruzione, dell’Università e della Ricerca

Fundação para a Ciência e a Tecnologia

Politecnico di Torino

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,General Physics and Astronomy,General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00033-022-01817-6.pdf

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