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Materials 2019, 12(2), 232; https://doi.org/10.3390/ma12020232

Asymptotic Homogenization Applied to Flexoelectric Rods

1
Department of Mathematics, University of Central Florida, 4393 Andromeda Loop N, Orlando, FL 32816, USA
2
Departamento de Mecánica de los Medios Continuos y T. Estructuras, E.T.S. de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, C.P. 28040 Madrid, Spain
3
Departamento de Matemática, Universidad de La Habana, San Lazaro y L, La Habana 10400, Cuba
4
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Alcaldía Álvaro Obregón, Apartado Postal 20-126, CDMX Mexico 01000, Mexico
*
Author to whom correspondence should be addressed.
Received: 6 December 2018 / Revised: 26 December 2018 / Accepted: 7 January 2019 / Published: 11 January 2019
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Abstract

In this manuscript, the equilibrium problem for a flexoelectric one-dimensional composite material is studied. The two-scales asymptotic homogenization method is used to derive the homogenized formulation of this problem. The manuscript offers a step-by-step methodology to derive effective coefficients and to solve local problems. As an illustrative example, results reported in the literature for piezoelectric composites are obtained as a particular case of the formulation derived here. Finally, three flexoelectric/piezoelectric composites are studied to illustrate the influence of the flexoelectric property on the effective coefficients and the global behavior of the structure. View Full-Text
Keywords: composite; flexoelectric; homogenization method composite; flexoelectric; homogenization method
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Guinovart-Sanjuán, D.; Merodio, J.; López-Realpozo, J.C.; Vajravelu, K.; Rodríguez-Ramos, R.; Guinovart-Díaz, R.; Bravo-Castillero, J.; Sabina, F.J. Asymptotic Homogenization Applied to Flexoelectric Rods. Materials 2019, 12, 232.

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