In a remarkable study, E. Cosserat and F. Cosserat [54] gave a systematic development of the mechanics of continuous media in which each point has the six degree of freedom of a rigid body. The orientation of a given particle of such a medium can be represented mathematically by the values of three mutually perpendicular unit vectors which Ericksen and Truesdell [76] called directors. In the 1960s, the subject matter was reopened in the works [81,110,228]. These early theories were discussed in Refs. 85,193,332. The Cosserat elastic continuum has been used as model for bones and for engineering materials like concrete and other composites (see [85] and references therein).