  In a geometrically non-linear Cosserat model for micro-polar elastic solids,
we insert dipole pairs of singularities into smooth maps and control the amount
of Cosserat energy needed to do so. We use this method to force an arbitrary
number of singular points into Cosserat-elastic solids by prescribing smooth
boundary data. Throughout this paper, we exploit connections between harmonic
maps and Cosserat-elastic solids, so that we are able to adapt and incorporate
ideas of R. Hardt and F.-H. Lin, as well as F. B\'ethuel.
