Theoretical model of homogenized piezoelectric materials with small non-collinear periodic cracks
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 thr...
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| Format: | Article |
| Language: | English |
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Gruppo Italiano Frattura
2017-09-01
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| Series: | Fracture and Structural Integrity |
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| Online Access: | https://www.fracturae.com/index.php/fis/article/view/1958 |
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| author | Jean-Marie Nianga Driss Marhabi |
| author_facet | Jean-Marie Nianga Driss Marhabi |
| author_sort | Jean-Marie Nianga |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f3e0f167ccde4542952408163334b5ff |
| institution | Kabale University |
| issn | 1971-8993 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | Gruppo Italiano Frattura |
| record_format | Article |
| series | Fracture and Structural Integrity |
| spelling | doaj-art-f3e0f167ccde4542952408163334b5ff2025-01-03T01:03:06ZengGruppo Italiano FratturaFracture and Structural Integrity1971-89932017-09-011142Theoretical model of homogenized piezoelectric materials with small non-collinear periodic cracksJean-Marie Nianga0Driss Marhabi1Pôle de Recherche « Structures & Matériaux », Hautes Etudes d’Ingénieur – (HEI), 13 rue de Toul, 59046 Lille Cedex, FrancePôle de Recherche « Structures & Matériaux », Hautes Etudes d’Ingénieur – (HEI), 13 rue de Toul, 59046 Lille Cedex, FranceAn 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.https://www.fracturae.com/index.php/fis/article/view/1958Piezoelectric materialAsymptotic expansionsHomogenizationVariational formulationPeriodic cracks |
| spellingShingle | Jean-Marie Nianga Driss Marhabi Theoretical model of homogenized piezoelectric materials with small non-collinear periodic cracks Fracture and Structural Integrity Piezoelectric material Asymptotic expansions Homogenization Variational formulation Periodic cracks |
| title | Theoretical model of homogenized piezoelectric materials with small non-collinear periodic cracks |
| title_full | Theoretical model of homogenized piezoelectric materials with small non-collinear periodic cracks |
| title_fullStr | Theoretical model of homogenized piezoelectric materials with small non-collinear periodic cracks |
| title_full_unstemmed | Theoretical model of homogenized piezoelectric materials with small non-collinear periodic cracks |
| title_short | Theoretical model of homogenized piezoelectric materials with small non-collinear periodic cracks |
| title_sort | theoretical model of homogenized piezoelectric materials with small non collinear periodic cracks |
| topic | Piezoelectric material Asymptotic expansions Homogenization Variational formulation Periodic cracks |
| url | https://www.fracturae.com/index.php/fis/article/view/1958 |
| work_keys_str_mv | AT jeanmarienianga theoreticalmodelofhomogenizedpiezoelectricmaterialswithsmallnoncollinearperiodiccracks AT drissmarhabi theoreticalmodelofhomogenizedpiezoelectricmaterialswithsmallnoncollinearperiodiccracks |