An 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.

Periodic homogenization in the context of structured deformations / Amar, Micol; Matias, Jos??; Morandotti, Marco; Zappale, Elvira. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - 73:4(2022). [10.1007/s00033-022-01817-6]

Periodic homogenization in the context of structured deformations

Marco Morandotti;Elvira Zappale
2022

Abstract

An 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.
File in questo prodotto:
File Dimensione Formato  
[032]-2022-Ama-Mat-Mor-Zap[ZAMP].pdf

accesso aperto

Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Creative commons
Dimensione 636.82 kB
Formato Adobe PDF
636.82 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2970767