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Archive of Applied Mechanics

, Volume 77, Issue 4, pp 229–239 | Cite as

Estimation of very narrow bounds to the behavior of nonlinear incompressible elastic composites

  • L. D. Pérez-Fernández
  • J. Bravo-Castillero
  • R. Rodríguez-Ramos
  • F. J. Sabina
Original

Abstract

Variational bounds for the effective behavior of nonlinear composites are improved by incorporating more-detailed morphological information. Such bounds, which are obtained from the generalized Hashin–Shtrikman variational principles, make use of a reference material with the same microstructure as the nonlinear composite. The geometrical information is contained in the effective properties of the reference material, which are explicitly present in the analytical formulae of the nonlinear bounds. In this paper, the variational approach is combined with estimates for the effective properties of the reference composite via the asymptotic homogenization method (AHM), and applied to a hexagonally periodic fiber-reinforced incompressible nonlinear elastic composite, significantly improving some recent results.

Keywords

Nonlinear composites Variational bounds Asymptotic homogenization Effective properties 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • L. D. Pérez-Fernández
    • 1
    • 2
  • J. Bravo-Castillero
    • 2
    • 3
  • R. Rodríguez-Ramos
    • 2
    • 3
  • F. J. Sabina
    • 4
  1. 1.Departamento de Física AplicadaInstituto de Cibernética, Matemática y FísicaCiudad de la HabanaCuba
  2. 2.Departamento de Ciencias BásicasInstituto Tecnológico y de Estudios Superiores de Monterrey, Campus Estado de MéxicoAtizapán de Zaragoza, Estado de MéxicoMéxico
  3. 3.Facultad de Matemática y ComputaciónUniversidad de La HabanaCiudad de la HabanaCuba
  4. 4.Instituto de Investigaciones en Matemáticas Aplicadas y en SistemasUniversidad Nacional Autónoma de MéxicoMéxico D. F.México

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