Computational implementation of Cosserat continuum

The recent trend towards miniaturisation has pushed the development of non-classical continuum mechanics theories intended to explain the behaviour of materials at small scales. In particular, a wide range of observed size dependent phenomena has been experimentally identified. Two issues arise in the numerical treatment of the theories. Firstly, in a displacement-based finite element approach the need appears for higher orders of continuity in the interpolation functions. Secondly, if non-linear-inelastic material response is expected the theories should be cast in rate form and the corresponding integration algorithms complete the implementation. In this paper we address both problems for the particular case of a Cosserat Couple Stress theory. We describe alternatives for the numerical treatment and then we extend the framework to the case of a rate independent inelastic – non-linear material behaviour. The equations are presented in its flow theory form together with integration algorithms.