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International audience; The question of the nonlinear response of brittle materials undergoing elastic damage is investigated here. Owing to the specific nature of microcracking, the macroscopic behaviour of these materials is complex, generally anisotropic owing to the possible preferential orientation of defects and multilinear because of the unilateral effect due to the transition between open and closed state of microcracks. A new three-dimensional macroscopic model outlined by Welemane and Cormery [1] has been proposed to account simultaneously for these both aspects. This paper intends to present in details the principles of such approach and to demonstrate its applicability to a stress-based framework. Based on a fabric tensor representation of the damage density distribution, the model provides a continuum and rigorous description of the contribution of defaults which avoids classical spectral decompositions and related inconsistencies. The model is also strongly micromechanically motivated, especially to handle the elastic moduli recovery that occurs at the closure of microcracks. The macroscopic theoretical framework proposed constitutes a general approach that leads in particular to predictions of a class of micromechanical models. The capacities of the approach are illustrated and discussed on various cases of damage configurations and opening–closure states, with a special attention to the differences with the strain-based framework and to the influence of the damage variables order.

International audience; The present paper deals with a micromechanical approach to modeling the time-dependent mechanical behavior of a class of cohesive geomaterials. The considered material is Callovo-Oxfordian argillite, which is mainly composed of three constituents: an elastoviscoplastic clay matrix, elastic quartz minerals, and elastic damaged calcite grains. The macroscopic constitutive law is obtained by adapting the incremental method proposed by Hill (J. Mech. Phys. Solids 1965; 13:89-101). Its unified formulation allows a description of not only the time-dependent behavior of the argillite but also its elastoplastic damage response. The developed model is first validated by comparison with finite element solutions and then it is applied to the prediction of argillites' macroscopic responses in connection with their mineralogical compositions. The validity of the model is checked through comparisons between the model's predictions and experimental data.

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.

This study deals with the macroscopic modelling of the mechanical behaviour of microcracked materials and particularly with the unilateral aspect of such damage which leads, at the closure of microcracks, to a partial damage deactivation. By means of a micromechanical analysis, the aim of this article is first to point out the influence of the opening–closure of microdefects on the effective elastic properties of a microcracked medium. According to these considerations,a new elastic moduli recovery condition at damage deactivation is proposed. The introduction of this condition within the anisotropic damage model proposed by Halm and Dragon, 1996 allows its micromechanical background to be extended while preserving its main advantages, in particular the continuity of the stress–strain response and the symmetry of the stiffness tensor.

International audience; In this paper, we present an original extension of an isotropic damage model for quasi-brittle materials and assess its predictive capabilities. The proposed model accounts not only for unilateral behavior related to the opening and closure of microcracks but also for inelastic strains reflecting the frictional sliding along closed microcracks. More importantly, owing to its careful mathematical formulation with a particular attention paid to the continuous differentiability of the underlined thermodynamic potential, the model ensures the continuity of the inelastic stress–strain response. First applications show that it is able to predict the asymmetric behavior and hysteretic response of microcracked materials such as concrete and some rocks

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.

The concern here is the macroscopic modeling of the brittle damage unilateral effect (due to the opening-closure of microcracks). Several formulations have been proposed in recent years to solve the problems pointed out by Chaboche (Int. J. Damage Mech. 1 (1992) 148). In this paper, we examine precisely two of these new formulations (Int. J. Damage Mech. 2 (1993) 311; Int. J. Damage Mech. 5 (1996) 384) and show that they still exhibit some major inconsistencies.