Homogenization estimates for fiber-reinforced elastomers with periodic microstructures

M. Brun, O. Lopez-Pamies, P. Ponte Castañeda

Research output: Contribution to journalArticlepeer-review


This work presents a homogenization-based constitutive model for the mechanical behavior of elastomers reinforced with aligned cylindrical fibers subjected to finite deformations. The proposed model is derived by making use of the second-order homogenization method [Lopez-Pamies, O., Ponte Castañeda, P., 2006a. On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: I-theory. J. Mech. Phys. Solids 54, 807-830], which is based on suitably designed variational principles utilizing the idea of a "linear comparison composite." Specific results are generated for the case when the matrix and fiber materials are characterized by generalized Neo-Hookean solids, and the distribution of fibers is periodic. In particular, model predictions are provided and analyzed for fiber-reinforced elastomers with Gent phases and square and hexagonal fiber distributions, subjected to a wide variety of three-dimensional loading conditions. It is found that for compressive loadings in the fiber direction, the derived constitutive model may lose strong ellipticity, indicating the possible development of macroscopic instabilities that may lead to kink band formation. The onset of shear band-type instabilities is also detected for certain in-plane modes of deformation. Furthermore, the subtle influence of the distribution, volume fraction, and stiffness of the fibers on the effective behavior and onset of macroscopic instabilities in these materials is investigated thoroughly.

Original languageEnglish (US)
Pages (from-to)5953-5979
Number of pages27
JournalInternational Journal of Solids and Structures
Issue number18-19
StatePublished - Sep 2007
Externally publishedYes


  • Fiber-reinforced composite
  • Homogenization
  • Hyperelasticity
  • Microstructures
  • Soft matter
  • Stability

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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