A micromechanically based couple-stress model of an elastic orthotropic two-phase composite

Frederic Bouyge, Iwona Jasiuk, Stéphane Boccara, Martin Ostoja-Starzewski

Research output: Contribution to journalArticle

Abstract

We determine couple-stress moduli and characteristic lengths of a two-dimensional matrix-inclusion composite, with inclusions arranged in a periodic square array and both constituents linear elastic of Cauchy type. In the analysis we replace this composite by a homogeneous planar, orthotropic, couple-stress continuum. A generalization of the original Mindlin's (1963) derivation of field equations for such a continuum results in two (not just one!) characteristic lengths. We evaluate the couple-stress properties from the response of a unit cell under several types of boundary conditions: displacement, displacement-periodic, periodic and mixed, and traction controlled. In the parametric study we vary the stiffness ratio of both phases to cover a range of different media from nearly porous materials through composites with very stiff inclusions. We find that the aforementioned boundary conditions result in hierarchies of orthotropic couple-stress moduli, whereas both characteristic lengths are fairly insensitive to boundary conditions, and fall between 0.12% and 0.22% of the unit cell size for the inclusions' volume fraction of 18%.

Original languageEnglish (US)
Pages (from-to)465-481
Number of pages17
JournalEuropean Journal of Mechanics, A/Solids
Volume21
Issue number3
DOIs
StatePublished - Dec 1 2002
Externally publishedYes

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)

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