Theoretical model of homogenized piezoelectric materials with small non-collinear periodic cracks

• Main Authors: Jean-Marie Nianga, Driss Marhabi
• Format: Article
• Language: English
• Published: Gruppo Italiano Frattura 2017-09-01
• Series: Frattura ed Integrità Strutturale
• Subjects: Piezoelectric material; Asymptotic expansions; Homogenization; Variational formulation; Periodic cracks
• Online Access: https://www.fracturae.com/index.php/fis/article/view/1958

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.