In the present study, we propose an evaluation of a non-linear homogenization model applied to hyperelastic composites having random microstructure. This modelling approach consists in a 3D implementation of the secondorder method introduced by Ponte Castañeda & Tiberio [1]. We first recall the basic principles of this method. Then, we investigate a composite made up of an hyperelastic matrix reinforced by spherical deformable or rigid particles.Computational issues of the micromechanical model are discussed and some obtained results allowto demonstrate the reinforcement effect of the particles. In order to provide a rigorous evaluation of the methodology, finite elements computations, on an unit cell, are performed and compared to the predictions of the model. Finally, a confrontation with experimental results is provided.

The present study is devoted to the development and validation of a non-linear homogenizationapproach of the mechanical behavior of Callovo-Oxfordian argillites. The material is modelled as an heterogeneous one composed of an elastoplastic clay matrix and of linear elastic or elastic damage inclusions. The macroscopic constitutive law is obtained by adapting the Hill-type incremental method [1]. The approach consists in formulating the macroscopic tangent operator of the material from the non-linearlocal behavior of its phases. Due to the matrix/inclusion morphology of the microstructure of the argillites, a Mori-Tanaka scheme is considered for the localization step. The developed model is first compared to Finite-Elements calculations and then validated and applied for the prediction of the macroscopic stress-strain responses of argillites.