  The Cosserat continuum is used in this paper to regularize the ill-posed
governing equations of the Cauchy/Maxwell continuum. Most available
constitutive models adopt yield and plastic potential surfaces with a circular
deviatoric section. This is a too crude an approximation which hinders the
application of the Cosserat continuum into practice, particularly in the
geotechnical domain. An elasto-plastic constitutive model for the linear
formulation of the Cosserat continuum is here presented, which features
non-associated flow and hardening/softening behaviour, whilst linear
hyper-elasticity is adopted to reproduce the recoverable response. For the
formulation of the yield and plastic potential functions, a definition of the
\textit{equivalent von Mises stress} is used which is based on Hencky's
interpretation of the von Mises criterion and also on the theory of
representations. The dependency on the Lode's angle of both the yield and
plastic potential functions is introduced through the adoption of a recently
proposed \textit{Generalized classical} criterion, which rigorously defines
most of the classical yield and failure criteria.
