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Variational principles for nonlinear piezoelectric materials

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Summary

In the present paper, we consider the behavior of nonlinear piezoelectric materials by generalization for this case of the Hashin-Shtrikman variational principles. The new general formulation used here differs from others, because, it gives the possibility to evaluate the upper and lower Hashin-Shtrikman bounds for specific physical nonlinearities of piezoelectric materials. Geometrical nonlinearities are not considered.

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Author notes

  1. J. Bravo-Castillero

    Present address: Facultad de Matemática y Computación, Universidad de la Habana, San Lázaro y L CP., 10400, Vedado, Habana, Cuba

Authors and Affiliations

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

    R. Rodríguez-Ramos & R. Guinovart-Díaz

  2. Composites Department, Moscow State University M. V. Lomonosov, Moscow, Russia

    B. E. Pobedria

  3. Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS), Universidad Nacional Autónoma de México, Circuito Escolar, Cd. Universitaria, México D.F., México

    P. Padilla

  4. Laboratoire de Modélisation en Mécanique, Université Pierre et Marie Curie. Case 162, UMR 7607 CNRS, 4 place Jussieu, 75252, Paris Cedex 05, France

    G. A. Maugin

  5. Instituto Tecnológico de Estudios Superiores de Monterrey, Campus Estado de México. División de Arquitectura e Ingeniería, Apartado Postal 6-3, Atizapán de Zaragoza, 52926, Estado de México, México

    J. Bravo-Castillero

Authors
  1. R. Rodríguez-Ramos
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  2. B. E. Pobedria
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  3. P. Padilla
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  4. J. Bravo-Castillero
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  5. R. Guinovart-Díaz
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  6. G. A. Maugin
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Corresponding author

Correspondence to G. A. Maugin.

Additional information

This work was sponsored by PAPIIT, DGAPA-UNAM IN103301. PNCB IBMFQ 09-2004 and, completed while one of the authors (RRR) was visiting the Laboratoire de Modélisation en Mécanique from Université Pierre et Marie Curie, Paris, while another one (G.A.M) benefited from the Max-Plank Award for International Cooperation (2002–2005).

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Rodríguez-Ramos, R., Pobedria, B., Padilla, P. et al. Variational principles for nonlinear piezoelectric materials. Archive of Applied Mechanics 74, 191–200 (2004). https://doi.org/10.1007/s00419-003-0319-0

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  • DOI: https://doi.org/10.1007/s00419-003-0319-0

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