Abstract
An analytical model for the homogenization of a piezoelectric material with small periodic fissures is proposed on the basis of the method of asymptotic expansions for the elastic displacement, the electric scalar potential and the test functions. Starting from the variational formulation of the three-dimensional problem of linear piezoelectricity, we have at first obtained that concerning a cracked piezoelectric structure, before the implementation of homogenized equations for a piezoelectric structure with a periodic distribution of cracks. It then follows, the characterization of the homogenized law between the mechanical strain and the electric potential, on one hand, and the mechanical stress and the electric displacement, on the other hand. Contrary to the previous investigations, the focus of this paper is the development of a mathematical model taking the non-parallelism of cracks into account.
Keywords
How to cite
APA
IEEE
MLA
Chicago
Harvard
Vancouver
BibTeX
RIS
Licence
May be shared and adapted, provided appropriate credit is given. Copyright © 2017 Fracture and Structural Integrity.
Copyright
Authors are allowed to retain both the copyright and the publishing rights of their articles without restrictions.
Open Access Statement
Fracture and Structural Integrity (F&SI) is an open-access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. This is in accordance with the DOAI definition of open access.
F&SI operates under the Creative Commons Licence Attribution 4.0 International (CC-BY 4.0). This allows to copy and redistribute the material in any medium or format, to remix, transform and build upon the material for any purpose, even commercially, but giving appropriate credit, providing a link to the license, and indicating if changes were made.