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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access published online on April 23, 2008
The Quarterly Journal of Mechanics and Applied Mathematics, doi:10.1093/qjmam/hbn010
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© The author 2008. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Homogenization of Magneto-Electro-Elastic Multilaminated Materials

Julián Bravo-Castillero and Reinaldo Rodríguez-Ramos

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

Houari Mechkour

( Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau Cedex, France )

José A. Otero

( Instituto de Cibernética, Matemática y Física, 15 No. 551, Vedado, CP 10400, Habana 4, Cuba )

Federico J. Sabina{dagger}

( Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-726, Delegación de Álvaro Obregón, 01000 México D.F., México )

{dagger} < fjs{at}mym.iimas.unam.mx>

Received 22 June 2007. Revise 22 February 2008.
  Abstract

In this work, based on the periodic unfolding homogenization technique, the limiting equations modelling the behaviour of three-dimensional magneto-electro-elastic periodic structures are rigorously established. The local problems and the corresponding homogenized coefficients of the elastic, dielectric, magnetic permittivity, piezoelectric, piezomagnetic and magneto-electric (ME) tensors are explicitly described. The homogenization model is exemplified for laminated composites and a unified general formula for all effective properties of periodic multilaminated magneto-electro-elastic composites is obtained. This formula is applied to investigate the global behaviour for the important case of transversely isotropic constituents and any finite number of layers in each periodic cell. Examples that provide theoretical evidence of the presence of both a product property and the ME effect are given.


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