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Unified formulae of variational bounds for multiphase anisotropic elastic composites

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Abstract

Using the spherical and deviator decomposition of the polarization and strain tensors, we present a general algorithm for the calculation of variational bounds of dimension d for any type of anisotropic linear elastic composite as a function of the properties of the comparison body. This procedure is applied in order to obtain analytical expressions of bounds for multiphase, linear elastic composites with cubic symmetry where the geometric shapes of the inclusions are arbitrary. For the validation, it can be proved that for the isotropic particular case, the bounds coincide with those recently reported by Gibiansky and Sigmund. On the other hand, based on this general procedure some, classical bounds reported by Hashin for transversely isotropic composites, are reproduced. Numerical calculations and some comparisons with other models and experimental data are shown.

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Authors and Affiliations

  1. Centro de Medicina y Complejidad, Instituto Superior de Ciencias Médicas “Carlos J. Finlay”, Carretera Central Oeste SN, Camaguey, Cuba

    H. Brito-Santana

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

    R. Rodríguez-Ramos, R. Guinovart-Díaz & J. Bravo-Castillero

  3. Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-726, Delegación de Álvaro Obregón, 01000, Mexico DF, Mexico

    F. J. Sabina

  4. Université Pierre et Marie Curie, Institut Jean Le Rond d’Alembert, UMR CNRS 7190, Case 162, 4 place Jussieu, 75252, Paris Cedex 05, France

    G. A. Maugin

Authors
  1. H. Brito-Santana
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  2. R. Rodríguez-Ramos
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  3. R. Guinovart-Díaz
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  4. J. Bravo-Castillero
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  5. F. J. Sabina
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  6. G. A. Maugin
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Corresponding author

Correspondence to R. Rodríguez-Ramos.

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Brito-Santana, H., Rodríguez-Ramos, R., Guinovart-Díaz, R. et al. Unified formulae of variational bounds for multiphase anisotropic elastic composites. Arch Appl Mech 79, 189–204 (2009). https://doi.org/10.1007/s00419-007-0197-y

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  • DOI: https://doi.org/10.1007/s00419-007-0197-y

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