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.