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Semi-analytic finite element method applied to short-fiber-reinforced piezoelectric composites

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Abstract

In this work, a 3D semi-analytical finite element method (SAFEM) is developed to calculate the effective properties of piezoelectric fiber-reinforced composites (PFRC). Here, the calculations are implemented in one-eighth of the unit cell to simplify the method. The prediction of the effective properties for periodic PFRC made of piezoceramic unidirectional fibers (PZT) with square and hexagonal space arrangements in a soft non-piezoelectric matrix (polymer) is reported as a way to validate the 3D approach. The limit case, when short fibers become long ones, allows us to compare with results reported in the literature. For the analysis of effective properties as a function of fiber relative length, two cases are considered: (i) constant volume fraction and (ii) constant fiber radius. The constant volume fraction case is of special interest because according to the Voigt–Reuss–Hill approximation, the effective properties should remain constant. Then, in order to analyze this case, mechanical and electric fields are also shown. The obtained results show a physically congruent behavior. Good coincidences are obtained by comparing with asymptotic homogenization and the representative volume element methods. The 3D SAFEM is also implemented to study the bone piezoelectric behavior with attention to the role of the mineralized phase on the effective \(d_{333}^{*}\) piezoelectric coefficient.

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Acknowledgements

L. E. Barraza de León would like to thank CONACYT for scholarship funding. YEA gratefully acknowledges the Program of Postdoctoral Scholarships of DGAPA from UNAM, México. HCM and YEA are grateful to the support of the CONACYT Basic Science Grant A1-S-9232. FJS acknowledges the funding of PAPIIT-DGAPA-UNAM IA100919.

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Authors and Affiliations

  1. Instituto de Ingeniería y Tecnología, Universidad Autónoma de Ciudad Juárez, Av. Del Charro 450 Norte Cd. Juárez, CP, 32310, Chihuahua, México

    L. E. Barraza de León & H. Camacho-Montes

  2. Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-126, 01000, Alcaldía Álvaro Obregón, CDMX, México

    Y. Espinosa-Almeyda & F. J. Sabina

  3. Tecnológico de Monterrey, Escuela de Ingeniería y Ciencias, CP 52926, Ciudad López Mateos, Estado de México, México

    J. A. Otero

  4. Facultad de Matemática y Computación, Universidad de La Habana, San Lázaro y L, Vedado, CP 10400, La Habana, Cuba

    R. Rodríguez-Ramos & J. C. López-Realpozo

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  1. L. E. Barraza de León
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  2. H. Camacho-Montes
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  3. Y. Espinosa-Almeyda
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  4. J. A. Otero
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  5. R. Rodríguez-Ramos
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Correspondence to H. Camacho-Montes.

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Communicated by Marcus Aßmus, Victor A. Eremeyev, and Andreas Öchsner.

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de León, L.E.B., Camacho-Montes, H., Espinosa-Almeyda, Y. et al. Semi-analytic finite element method applied to short-fiber-reinforced piezoelectric composites. Continuum Mech. Thermodyn. 33, 1957–1978 (2021). https://doi.org/10.1007/s00161-021-01016-0

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