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This paper reviews some aspects of the formulation of the constitutive behavior of a saturated porous material in isothermal evolutions in the domain of large strains. First, the results concerning the nonporous solid are recalled. Then, the poroelastic and poro-elastoplastic behaviors at large strains are successively considered. When the solid phase is elastic at large strains, a micro-macro approach shows that the free energy of the skeleton is a macroscopic thermodynamic potential. The latter depends on the macroscopic strain of the skeleton and on the lagrangian porosity, which can be interpreted as macroscopic state variables. When the solid is elastoplastic at large strains, a theory of finite poro-elastoplasticity is proposed within a macroscopic thermodynamic framework. The homogenization techniques allow to clarify some aspects of the formulation of the macroscopic behavior. In particular, the validity of the effective stress principle in finite poroelasticity and poroplasticity is established when the solid phase is incompressible. Even if the macroscopic strain applied to an elementary volume is infinitesimal, the strain field at the microscopic scale may not be infinitesimal. Hence, the simulation of the macroscopic behavior of this elementary volume in the framework of a micro-macro approach must take into account possible large strains at the microscopic scale. Cet article examine quelques aspects de la formulation du comportement d'un milieu poreux saturé en évolution isotherme dans le domaine des transformations finies. Après avoir rappelé les résultats propres aux solides non poreux, on s'intéressera successivement aux comportements poroélastique et poro-élastoplastique. Si la phase solide qui constitue le squelette présente un comportement élastique dans le domaine des grandes déformations, un passage micro-macro démontrera que l'énergie libre du squelette constitue un potentiel thermodynamique pour le comportement macroscopique. Les arguments de ce potentiel sont la déformation macroscopique du squelette ainsi que la porosité lagrangienne. Ces deux quantités s'interprètent commes des variables d'état macroscopiques. Dans le cas où le comportement du solide est élastoplastique en grandes déformations, on propose un cadre thermodynamique permettant de formuler une théorie de la poroplasticité finie. Les techniques de changement d'échelle permettent de clarifier certains aspects de la formulation du comportement macroscopique. En particulier, la validité du concept de contrainte effective en poroélasticité et en poroplasticité finies est établie lorsque la phase solide est incompressible. Même lorsque la déformation macroscopique imposée à un élément de volume de milieu poreux est infinitésimale, le champ de déformation à l'échelle microscopique peut être non infinitésimal. De ce fait, la simulation du comportement macroscopique de ce volume élémentaire dans le cadre d'un passage micro-macro doit être effectuée en tenant compte de transformations finies à l'échelle microscopique. Ce point est illustré par l'exemple du chargement Sdométrique.

In order to address the question of oil-induced microfracturing, we propose under specific assumptions (plane circular kerogen flake surrounded by an homogeneous microfractured porous medium) an analytical method for the determination of the oil pressure increase. It is based on a mechanical modelling of the kerogen-oil-rock interaction at the microscopicscale of a kerogen particle. It is shown that the oil pressure tends towards an asymptotic value when the chemical transformation of kerogen is completed. The effect of the macroscopic stress variation during oil formation process proves to be negligible. However, this effect must be taken into account for describing the evolution of oil pressure at earlier stages of oil formation process. The increase in burial depth induces an increase of oil pressure as well as a variation of the macroscopic stress which both determine the microscopic stress field. The possibility of microfracturing depends on the position of the microscopic stress state with respect to the fracture criterion. If the duration of the oil formation process is short enough, so that the macroscopic stress change associated with the corresponding (small) burial depth increase can be neglected, it is found that microfracturing is likely for the usual values of rock tensile strength. However, in the general case, neglecting the macroscopic stress change can significantly overestimate the possibility of fracture initiation due to oil-pressure increase. Considering now the macroscopicscale of the source bed, the evolution equation of the oil pressure are derived within the framework of Biot's poroelasticity theory. The oil pressure rate proves to be the sum of a diffusion term which accounts for oil migration within the source bed, and of two source terms respectively associated with the volume expansion tendency of the kerogen - oil transformation and the overburden pressure increase. Dans le but d'étudier le problème de la microfracturation induite par la génération des hydrocarbures dans les roches mères, nous proposons une méthode analytique pour déterminer l'évolution de la pression de l'huile. Cette méthode est basée sur une modélisation mécanique des interactions kérogène-huile-roche à l'échelle microscopique. Il est montré que la pression de l'huile tend vers une valeur asymptotique quand la réaction de transformation du kérogène en huile s'achève. Les variations des contraintes macroscopiques pendant la formation de l'huile ont des effets faibles. Cependant, ils doivent être considérés pour décrire correctement l'évolution de la pression de l'huile au stade précoce de la génération. L'augmentation de l'enfouissement provoque une augmentation de la pression de l'huile ainsi qu'une augmentation des contraintes macroscopiques. Cela conditionne l'évolution du champ de contraintes microscopiques. La possibilité de microfracturation dépend de la position du champ de contraintes microscopiques par rapport au critère de rupture. Si la durée de la transformation du kérogène en huile est suffisamment courte, de sorte que l'on puisse négliger la variation du champ de contraintes macroscopiques induite par la variation de l'enfouissement, alors, on montre que pour des valeurs usuelles des paramètres mécaniques, la microfracturation est possible. Néanmoins, de façon plus générale, le fait de négliger les variations du champ de contraintes macroscopiques conduit à une surestimation des possibilités de microfracturation induite par l'augmentation de la pression de l'huile. À l'échelle macroscopique (de la roche mère), l'équation qui décrit l'évolution de la pression de l'huile est écrite dans le cadre de la théorie poroélastique de Biot. L'évolution de la pression est donnée par la somme d'un terme de diffusion qui provient de la migration de l'huile dans la roche, et de deux termes respectivement associés à l'expansion volumique de la transformation du kérogène en huile et à l'augmentation de la charge due à l'enfouissement.

Les contributions successives de différents auteurs ont permis d'identifier les phénomènes mis en jeu dans la compaction des sédiments, puis de proposer des modélisations mécaniques cohérentes de ce processus. On s'intéresse ici aux non-linéarités géométriques dues à la forte diminution de la porosité: elles imposent de renoncer à employer la déformation de Green-Lagrange linéarisée. On adopte une loi de comportement adaptée aux grandes transformations d'un milieu poreux élastique dont les constituants sont incompressibles pour étudier la diminution de porosité liée aux phénomènes purement mécaniques intervenant dans la compaction. The numerous works devoted to the phenomena involved in the compaction of sediments have led to a good understanding and to mechanically consistent modellings of this process. During compaction, large reduction of porosity occurs and the sediments undergo large strains : in this context, the usual linearized Green-Lagrange strain tensor is no longer relevant. Using the constitutive law of a poroelastic medium (made of incompressible constituents) at large strains, we discuss the influence of geometrical nonlinearities in the study of purely mechanical compaction.

The aim of this paper is to model the viscoelastic properties of micro-cracked materials based on the homogenization micro-macro approach. The isotropic case with random orientation distribution of micro-crack in Burgers non-ageing linear viscoelastic solid was previously modeled. However, in many cases, micro-cracks appear to be parallel and the macroscopic behavior is transversely isotropic. An alternative effective transversely isotropic Burgers model is developed to model the behavior of such materials for the cases of open cracks. For this anisotropic case, the Burgers model for the macroscopic viscoelastic behavior of the micro-cracked materials depends on 20 viscoelastic parameters which are functions of the damage parameter and of the viscoelastic properties of the solid phase. In this study, the evolution of all 20 damage viscoelastic parameters as functions of the crack density is detailed based on a dilute-stress homogenization approach. The use of the same Burgers viscoelastic model as non-cracked material to model the viscoelastic behavior of micro-cracked material is an approximation. This approximation is carried out in short- and long-term behaviors. However, the comparison of this approximation with the exact solution in the case of 1D traction loading showed an excellent validation of this approach in transient situation. [ABSTRACT FROM AUTHOR]

In the case of micro-cracked viscoelastic materials, the numerical approach is required to solve the problem of crack propagation. The step-by-step method is used to model, using the finite element method, a morphologically representative pattern of the media. The computation of the effective behaviour of the material in the case without crack propagation shows a very good validation with respect to the Burger effective model obtained by the analytical method. The case of crack propagation is solved numerically considering a morphologically representative pattern containing a single crack. We also develop the concept of critical rate of kinematic loading and of asymptotic damage. [ABSTRACT FROM PUBLISHER]

A general three-dimensional micromechanical approach to modeling anisotropic damage of brittle materials such as concrete, rocks, or certain ceramics is presented. Damage is analyzed as a direct consequence of microcracks growth. Following a rigorous scale change methodology, the macroscopic free energy of the microcracked medium is built considering either open and closed microcracks. Moreover, the microcracks opening/closure criterion as well as the moduli recovery conditions (unilateral effects) are addressed in stress-based and strain-based formulations. An alternative derivation of the homogenized properties, based on the well-known Eshelby method, is also presented and extended here to closed cracks. From the micromechanical analysis, an energy-based yield condition is formulated and illustrated in various stress subspaces. Assuming that the normality rule applies, we then present the damage evolution law and the rate form of the constitutive model. The main capabilities and advantages of the micromechanical model are illustrated through various examples in which material microstructure evolutions are presented. [ABSTRACT FROM AUTHOR]

The successful design of ceramic bone biomaterials is challenged by two competing requirements: on the one hand, such materials need to be stiff and strong, which would suggest a low porosity (of pore sizes in the 10-100 microm range) to be targeted; on the other hand, bone biomaterials need to be bioactive (in particular vascularized), which suggests a high porosity of such materials. Conclusively, reliable information on how porosity drives the stiffness and strength properties of ceramic bone biomaterials (tissue engineering scaffolds) is of great interest. In this context, mathematical models are increasingly being introduced into the field. Recently, self-consistent continuum micromechanics formulations have turned out as expressedly efficient and reliable tools to predict hydroxyapatite biomaterials' stiffness and strength, as a function of the biomaterial-specific porosity, and of the 'universal' properties of the individual hydroxyapatite crystals: their stiffness, strength and shape. However, the precise crystal shape can be suitably approximated by specific ellipsoidal shapes: while it was shown earlier that spherical shapes do not lead to satisfactory results, and that acicular shapes are an appropriate choice, we here concentrate on disc-type crystal shape as, besides needles, plates are often reported in micrographs of hydroxyapatite biomaterials. Disc-based model predictions of a substantial set of experimental data on stiffness and strength of hydroxyapatite biomaterials almost attain the quality of the very satisfactory needle-based models. This suggests that, as long as the crystal shape is clearly non-spherical, its precise shape is of secondary importance if stiffness and strength of hydroxyapatite biomaterials are predicted on the basis of continuum micromechanics, from their micromorphology and porosity.

Both clays and calcium silicate hydrates(the main hydration products of Portland cements) exhibit a microstructure made up of lamellar particles. The microscopic mechanism responsible for the macroscopic creep of such materials is often described as the relative sliding of the sheets. This paper proposes a micromechanical approach to estimate the macroscopic creep behavior rising from this microscopic mechanism. The asymptotic evolution of creep at both short- and long-term is especially investigated. More precisely, a non-vanishing initial elastic strain is retrieved. At long-term, a threshold on porosity appears. At lower porosities, the creep evolution admits an asymptotic strain. At higher porosities, it admits an asymptotic strain rate.

Expansive reactions damage porous materials through the formation of reaction products of a volume in excess of the available space left by the reactants and the natural porosity of the material. This leads to pressurizing the pore space accessible to the reaction products, which differs when the chemical reaction is through-solution or topochemical or both in nature. This paper investigates expansive reactions from a micromechanical point of view, which allows bridging the scale from the local chemo-mechanical mechanisms to the macroscopically observable stress-free expansion. In particular, the study of the effect of morphology of the pore space, in which the chemical expansion occurs locally, on the macroscopically observable expansion is the main focus of this paper. The first part revisits the through-solution and the topochemical reaction mechanism within the framework of micro-macro-homogenization theories, and the effect of the microscopic geometry of pores and microcracks in the solid matrix on the macroscopic chemical expansion is examined. The second part deals with the transition from a topochemical to a through-solution-like mechanism that occurs in a solid matrix with inclusions (cracks, pores) of different morphology.