Effective elastic properties of periodic composite medium

Israel Cohen, David J. Bergman

Research output: Contribution to journalArticlepeer-review


A new method is presented for calculating the bulk effective elastic stiffness tensor of a two-component composite with a periodic microstructure. The basic features of this method are similar to the one introduced by Bergman and Dunn (1992) for the dielectric problem. It is based on a Fourier representation of an integro-differential equation for the displacement field, which is used to produce a continued-fraction expansion for the elastic moduli. The method enabled us to include a much larger number of Fourier components than some previously proposed Fourier methods. Consequently our method provides the possibility of performing reliable calculations of the effective elastic tensor of periodic composites that are neither dilute nor low contrast, and are not restricted to arrays of nonoverlapping inclusions. We present results for a cubic array of nonoverlapping spheres, intended to serve as a test of quality, as well as results for a cubic array of overlapping spheres and a two dimensional hexagonal array of circles (a model for a fiber reinforced material) for comparison with previous work.

Original languageEnglish
Pages (from-to)1433-1457
Number of pages25
JournalJournal of the Mechanics and Physics of Solids
Issue number8
StatePublished - Aug 2003


  • Anisotropic material
  • Elastic material
  • Inhomogeneous material
  • Microstructures


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