Summary: Some mean-field approximation methods are considered, with the objective to transfer any arbitrary local plasticity constitutive description to an overall analytical continuum description. Both correction methods of the Transformation Field Analysis (using elasticity-based accomodation rules), the Incremental Tangent and the Affine methods are compared. For the two last methods, the important problem of the plasticity induced anistotropy in the tangent space is addressed, together with some possible justifications of using instead isotropic approximations.
A numerical study is performed, based on unit cell finite element analyses in the context of periodic homogenization. It delivers reference solutions for the overall stress-strain responses with various local constitutive behaviours. In accordance with some previous findings, the systematic comparisons of the mean-field approximation methods leads to the conclusion that only the isotropic approximations of the tangent operators are able to deliver acceptable overall responses.