Viscoelastic effective properties for composites with rectangular cross-section fibers using the asymptotic homogenization method

  • Oscar L. Cruz-González
  • Reinaldo Rodríguez-Ramos
  • José A. Otero
  • Julián Bravo-Castillero
  • Raúl Guinovart-Díaz
  • Raúl Martínez-Rosado
  • Federico J. Sabina
  • Serge Dumont
  • Frederic Lebon
  • Igor Sevostianov
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 89)


The present work deals with the estimation of the linear viscoelastic effective properties for composites with periodic structure and rectangular cross-section fibers, using the two-scale asymptotic homogenization method (AHM). As a particular case, the effective properties for a layered medium with transversely isotropic properties are obtained. Two times the homogenization method, in different directions, according to the geometrical configuration of the composite material is applied for deriving the analytical expressions of the viscoelastic effective properties for a composite material with rectangular cross-section fibers, periodically distributed along one axis. In addition to that, models with different creep kernels, in particular, the Rabotnov’s kernel are analyzed. Finally, the numerical computation of the effective viscoelastic properties is developed for the analysis of the results. Moreover, a numerical algorithm using FEM is developed in the present work. Comparisons with other approaches are given as a validation of the present model.


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The authors would like to be grateful to University of Matanzas and Tecnologico de Monterrey, Escuela de Ingenieria y Ciencias, Atizapan de Zaragoza, Estado de Mexico, for its support. France-Cuba project "Partenariat Hubert Curien franco-cubain Carlos J. Finlay" 2017-2018 and Proyecto Nacional de Ciencias Básicas 2017-2019 are gratefully acknowledged. Thanks to Departamento de Matemáticas y Mecánica IIMAS-UNAM and FENOMEC for their support and Ramiro Chávez Tovar and Ana Pérez Arteaga for computational assistance.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Oscar L. Cruz-González
    • 1
  • Reinaldo Rodríguez-Ramos
    • 2
  • José A. Otero
    • 3
  • Julián Bravo-Castillero
    • 2
  • Raúl Guinovart-Díaz
    • 2
  • Raúl Martínez-Rosado
    • 3
  • Federico J. Sabina
    • 4
  • Serge Dumont
    • 5
  • Frederic Lebon
    • 6
  • Igor Sevostianov
    • 7
  1. 1.Facultad de Ciencias Técnicas, Departamento de MatemáticaUniversidad de MatanzasMatanzasCuba
  2. 2.Facultad de Matemática y ComputaciónUniversidad de La HabanaLa HabanaCuba
  3. 3.Tecnologico de Monterrey, Escuela de Ingenieria y CienciasAtizapan de ZaragozaMéxico
  4. 4.Instituto de Investigaciones en Matemáticas Aplicadas y en SistemasUniversidad Nacional Autónoma de MéxicoApartadoMéxico
  5. 5.Institut de Mathématiques Alexander Grothendieck, CNRS, UMR 5149Université de NîmesMontpellier Cedex 5France
  6. 6.CNRS, Centrale Marseille, LMAAix-Marseille UniversityMarseille Cedex 13France
  7. 7.Department of Mechanical and Aerospace EngineeringNew Mexico State UniversityLas CrucesUSA

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