In this paper, constitutive relations are derived for a linear Cosserat continuum possessing hemitropic symmetry. In such a continuum, the microstructure has a screwlike property, or handedness, and can support initial couple stresses of twist. These initial stresses serve as a model for cohesion. The introduction of free boundaries in such a medium brings about an unbalancing of the internal “cohesive” forces which results in a highly localized skin effect. This skin effect is represented by an outward, or inward, motion of a boundary layer, which is accompanied by microtwisting. A qualitative comparison is obtained with a specific solution based upon the linear elastic dislocation theory.

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