A variational approach of homogenization of piezoelectric composites towards piezoelectric and flexoelectric effective media

Nagham Mawassy (1) , Hilal Reda (1, 2) , Jean-Francois Ganghoffer (3) , Victor A. Eremeyev (4, 5) , Hassan Lakiss (1)

1 LU / ULB - الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth]
2 BIU - International University of Beirut
3 LEM3 - Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux
4 GUT - Gdańsk University of Technology
5 Lobachevsky State University [Nizhni Novgorod]

The effective piezoelectric properties of heterogeneous materials are evaluated in the context of periodic homogenization, whereby a variational formulation is developed, articulated with the extended Hill macrohomogeneity condition. The entire set of homogenized piezoelectric moduli is obtained as the volumetric averages of the microscopic properties of the individual constituents weighted by the displacement and polarization localization operators. This framework is extended in a second part of the paper to the computation of the flexoelectric effective properties, thereby accounting for higher gradient effects that may be induced by a strong contrast of properties of the composite constituents. The effective properties of inclusion-based composites are evaluated numerically as an illustration of the general homogenization theory and the respective effect of the volume fraction and relative tensile modulus of the reinforcement is assessed numerically.

Mots clés: Piezoelectricity; Flexoelectricity; Homogenization; Variational principles; Effective properties; Composite materials

Domaines: Sciences de l'ingénieur [physics]

Nagham Mawassy, Hilal Reda, Jean-Francois Ganghoffer, Victor A. Eremeyev, Hassan Lakiss. A variational approach of homogenization of piezoelectric composites towards piezoelectric and flexoelectric effective media. International Journal of Engineering Science, 2021, 158, pp.103410. ⟨10.1016/j.ijengsci.2020.103410⟩. ⟨hal-03493577⟩