Estimating the overall properties of heterogeneous Cosserat materials

Classical homogenization methods do nor account for size effects in the effective properties of polycrystals: they do not predict the influence of grain size nor the width of shear bands in localization phenomena. The polycrystal can be regarded as an example of a heterogeneous Cosserat material. A method is proposed to estimate the effective properties of aggregates of Cosserat media. A validation of the methodology is given in the case of linear Cosserat elasticity. Some steps towards an extension of the self-consistent scheme to Cosserat materials are then presented.