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The present study is devoted to the development and validation of a nonlinear homogenization approach of the mechanical behavior of Callovo-Oxfordian argillites. The material is modeled as an heterogeneous composite composed of an elastoplastic clay matrix and of linear elastic or elastic damage inclusions. The macroscopic constitutive law is obtained by adapting the incremental method proposed by Hill [Hill, R., 1965. Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids 13, 89–101]. The approach consists in formulating the macroscopic tangent operator of the material by considering the nonlinear local behavior of each phase. Due to the matrix/inclusion morphology of the microstructure of the argillite, a Mori–Tanaka scheme is considered for the localization step. The developed model is first compared to Finite Element calculations and then validated and applied for the prediction of the macroscopic stress–strain responses of argillites.

We consider isotropic elastic-damage behaviour such that the evolution law of the unique scalar internal variable characterizing material damage is associative (“ d -associativex201D; model). Two particular variants of modelling are considered. More precisely, and because of some analogies between these models and non-associative plasticity, we attempt to compare the loss of positiveness of second-order work and the localization criteria. These criteria are written in terms of critical damage. Thus, the damage value at loss of positiveness of second-order work is explicitly calculated in three-dimensional and plane strain cases. The procedure leading to the damage value at localization in the plane strain case is also presented. Both criteria are then compared for some loading paths. The results obtained indicate the localization occurring before loss of positiveness of the second-order work for some loading paths for one of two models. The same loading paths were tested with the other isotropic elastic-damage model; it is shown that localization always occurs after the loss of positiveness of second-order work (i.e. in softening phase). To endow this result with more generality, we then consider the problem of localization through a spectral analysis which finally shows that localization cannot take place in the hardening phase.