Elastoviscoplastic constitutive frameworks for generalized continua

A unifying thermomechanical constitutive framework for generalized continua including additional degrees of freedom or/and the second gradient of displacement is presented. Based on the analysis of the dissipation, state laws, flow rules and evolution equations are proposed for Cosserat, strain gradient and micromorphic continua. The case of the gradient of internal variable approach is also incorporated by regarding the nonlocal internal variable as an actual additional degree of freedom. The consistency of the continuum thermodynamical framework is ensured by the introduction of a viscoplastic pseudo-potential of dissipation, thus extending the classical class of so-called standard material models to generalized continua. Variants of the higher order and higher grade theories are also reported based on the explicit introduction of the plastic strain tensor as additional degree of freedom. Within this new class of models, called here gradient of strain models, one recognizes the fact that, in a second grade theory for instance, the plastic part of the strain gradient can be identified with the gradient of plastic strain. Simple examples dealing with bending and shearing of Cosserat or second grade media are given to illustrate two types of extensions of classical J(2)-plasticity : single-criterion and multi-mechanism generalized elastoplasticity. Finally, formulations at finite deformation of the proposed models are provided focusing on proper decompositions of Cosserat curvature, strain gradient and gradient of micromorphic deformation into elastic and viscoplastic parts.