  In this paper, we examine the recently developed skew-symmetric couple stress
theory and demonstrate its inner consistency, natural simplicity and
fundamental connection to classical mechanics. This hopefully will help the
scientific community to overcome any ambiguity and skepticism about this
theory, especially the validity of the skew-symmetric character of the
couple-stress tensor. We demonstrate that in a consistent continuum mechanics,
the response of infinitesimal elements of matter at each point decomposes
naturally into a rigid body portion, plus the relative translation and rotation
of these elements at adjacent points of the continuum. This relative
translation and rotation captures the deformation in terms of stretches and
curvatures, respectively. As a result, the continuous displacement field and
its corresponding rotation field are the primary variables, which remarkably is
in complete alignment with rigid body mechanics, thus providing a unifying
basis. For further clarification, we also examine the deviatoric symmetric
couple stress theory that, in turn, provides more insight on the fundamental
aspects of consistent continuum mechanics.
