Cosserat Media

In this chapter we discuss the three-dimensional Cosserat-type theories of continua. Originally this approach belongs to Cosserat brothers, Eugèn and François, who introduced an elastic media with kinematically independent translational and rotational degrees of freedom in their centurial book “Théorie des corps déformables” (Cosserat and Cosserat, 1909). Within the framework of the Cosserat media each point of the media can be represented as an infinitesimal rigid body. This means that in this media there exist stresses and couple stresses as responses for translational and rotational degrees of freedom. These characteristic features of the Cosserat continuum model give a possibility to describe more complex media, for example, micro-inhomogeneous materials, polycrystalline and cellular solids, foams, lattices, masonries, particle assemblies, magnetic rheological fluids, liquid crystals, etc. The aim of this chapter consists of a brief presentation of basics of Cosserat continuum mechanics including kinematics, dynamics and constitutive modeling