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Homogenized Stiffnesses of Periodic Fibre-Reinforced Composites

  • Conference paper
IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 113))

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Abstract

A two-phase fibre-reinforced composite is studied here, whose constituents are isotropic elastic arranged in a hexagonal array. The asymptotic homogenization method, applied to get the overall properties of this composite, yields exact closed-form solutions, which are amenable to a relatively easy computation. Limiting cases of rigid and empty fibres are considered. Hill’s universal relations follow from the formulae. The exact formulae explicitly display Avellaneda and Swart’s micro-structural parameters, which have a physical meaning, and provide formulae for them. A comparison between the hexagonal and square geometries is given.

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Author information

Authors and Affiliations

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

    Julian Bravo-Castillero, Raúl Guinovart-Diaz & Reinaldo Rodriguez-Ramos

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

    Federico J. Sabina

  3. Posgrado en Ciencias de la Tierra, U.N.A.M., Ciudad Universitaria, 04510, México, D.F., México

    Oscar C. Valdiviezo-Mijangos

  4. Campus Estado de México, División de Arquitectura e Ingenier’ia, Instituto Tecnológico de Estudios Superiores de Monterrey, Apartado Postal 6-3, Atizapán, 52926, México

    Julian Bravo-Castillero

  5. Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas, 152, Col. San Bartolo Atepehuacan, Del. G.A. Madero, 07730, México, D.F., México

    Oscar C. Valdiviezo-Mijangos

Authors
  1. Julian Bravo-Castillero
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  2. Raúl Guinovart-Diaz
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  3. Reinaldo Rodriguez-Ramos
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  4. Federico J. Sabina
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  5. Oscar C. Valdiviezo-Mijangos
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Editor information

Editors and Affiliations

  1. University of Liverpool, UK

    A. B. Movchan

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© 2003 Kluwer Academic Publishers

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Bravo-Castillero, J., Guinovart-Diaz, R., Rodriguez-Ramos, R., Sabina, F.J., Valdiviezo-Mijangos, O.C. (2003). Homogenized Stiffnesses of Periodic Fibre-Reinforced Composites. In: Movchan, A.B. (eds) IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics. Solid Mechanics and Its Applications, vol 113. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2604-8_37

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  • DOI: https://doi.org/10.1007/1-4020-2604-8_37

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1780-3

  • Online ISBN: 978-1-4020-2604-1

  • eBook Packages: Springer Book Archive

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