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

The study reported in this paper concerns the determination of couple-stres s moduli and characteristic lengths of heterogeneous materials. The study i s set in the context of a planar (two-dimensional), two-phase composite wit h linear non-couple-stress (classical), elastic constituents, with a single microstructural length scale (inclusion spacing) in an equilateral triangu lar array. We use an approach which allows a replacement of this composite by an approximating couple-stress continuum. We determine the effective mat erial parameters from the response of a unit cell under either displacement , displacement-periodic, or traction boundary conditions. We carry out comp utations of all the moduli by varying the stiffness ratio of both phases, s o as to cover a range of very different materials from porous solids throug h composites with rigid inclusions. It is found that the three boundary con ditions result in hierarchies of couple-stress moduli. In addition, we obse rve from our numerical computations that these three boundary conditions al so result in a hierarchy of characteristic lengths. (C) 2001 Elsevier Scien ce Ltd. All rights reserved.