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

Abstract 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.