A micropolar isotropic plasticity formulation for non-associated flow rule and softening featuring multiple classical yield criteria

The Cosserat continuum is very effective in regularizing the ill-posed governing equations of the Cauchy/Maxwell continuum. An elasto-plastic constitutive model for the linear formulation of the Cosserat continuum is here presented, which features non-associated flow, hardening/softening behaviour and multiple yield and plastic potential surfaces, whilst linear hyper-elasticity is adopted to reproduce the recoverable response. For the definition of the yield and plastic potential functions the equivalent von Mises stress is formulated using energy considerations and the theory of representations, the latter being also used to retrieve an expression for the Lode’s angle. The recent Generalized classical criterion is then used to define the yield and plastic potential functions so that Lode’s angle dependent deviatoric sections can be used.