Effective Coefficients and Local Fields of Periodic Fibrous Piezocomposites with 622 Hexagonal Constituents

  • Ransés Alfonso-Rodríguez
  • Julián Bravo-Castillero
  • Raúl Guinovart-Díaz
  • Reinaldo Rodríguez-Ramos
  • Renald Brenner
  • Leslie D. Pérez-Fernández
  • Federico J. Sabina
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 89)


The asymptotic homogenization method is applied to a family of boundary value problems for linear piezoelectric heterogeneous media with periodic and rapidly oscillating coefficients.We consider a two-phase fibrous composite consisting of identical circular cylinders perfectly bonded in a matrix. Both constituents are piezoelectric 622 hexagonal crystal and the periodic distribution of the fibers follows a rectangular array. Closed-form expressions are obtained for the effective coefficients, based on the solution of local problems using potential methods of a complex variable. An analytical procedure to study the spatial heterogeneity of the strain and electric fields is described. Analytical expressions for the computation of these fields are given for specific local problems. Examples are presented for fiber-reinforced and porous matrix including comparisons with fast Fourier transform (FFT) numerical results.


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Support provided by the French Priority Solidarity Fund (Campus France FSP Cuba 29896TD), the Brazilian Coordination for the Improvement of Higher Education Personnel (Project CAPES 88881.030424/2013-01), and the CoNaCyT 129658 is gratefully acknowledged. The authors are also grateful to Ana Pérez Arteaga and Ramiro Chávez for computational support. JB acknowledges the Cátedra Extraordinaria IIMAS and PREI-DGAPA, UNAM.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Ransés Alfonso-Rodríguez
    • 1
  • Julián Bravo-Castillero
    • 2
    • 3
  • Raúl Guinovart-Díaz
    • 2
  • Reinaldo Rodríguez-Ramos
    • 2
  • Renald Brenner
    • 4
  • Leslie D. Pérez-Fernández
    • 5
  • Federico J. Sabina
    • 3
  1. 1.Department of MathematicsUniversity of Central FloridaOrlandoUSA
  2. 2.Facultad de Matemática y ComputaciónUniversidad de La HabanaLa HabanaCuba
  3. 3.Instituto de Investigaciones en Matemáticas Aplicadas y en SistemasUniversidad Nacional Autónoma de MéxicoDelegación Álvaro ObregónMéxico
  4. 4.Institut Jean Le Rond d’AlembertSorbonne Université, Centre National de la Recherche ScientifiqueParisFrance
  5. 5.Departamento de Matemática e Estatística, Instituto de Física e MatemáticaUniversidade Federal de PelotasPelotasBrazil

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