Continua with microstructure: Cosserat theory

A brief description of the Cosserat continuum theory is presented. In the Introduction the history of the evolution of the theory is presented followed with some examples where the differences between the classical and Cosserat continua are more evident and the main areas of application. The formulation of the Cosserat continuum is then presented followed with the description and the equations of Cosserat elastoplasticity. Particular expressions are given for Mohr-Coulomb non-associative elastoplasticity. Finally and example of a simple Cosserat elastic problem that of a Timoshenko beam is presented to demonstrate the effects of the theory on the bending rigidity of a beam.