Micromechanically based couple-stress model of an elastic two-phase composite

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The study reported in this paper concerns the determination of couple-stress moduli and characteristic lengths of heterogeneous materials. The study is set in the context of a planar (two-dimensional), two-phase composite with linear non-couple-stress (classical), elastic constituents, with a single microstructural length scale (inclusion spacing) in an equilateral triangular array. We use an approach which allows a replacement of this composite by an approximating couple-stress continuum. We determine the effective material parameters from the response of a unit cell under either displacement, displacement-periodic, or traction boundary conditions. We carry out computations of all the moduli by varying the stiffness ratio of both phases, so as to cover a range of very different materials from porous solids through composites with rigid inclusions. It is found that the three boundary conditions result in hierarchies of couple-stress moduli. In addition, we observe from our numerical computations that these three boundary conditions also result in a hierarchy of characteristic lengths.

Original languageEnglish (US)
Pages (from-to)1721-1735
Number of pages15
JournalInternational Journal of Solids and Structures
Issue number10-13
StatePublished - Mar 2001
Externally publishedYes

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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