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 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.