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

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 e€ective 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 sti€ness ratio of both phases, so as to cover a range of very di€erent 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