Micromechanical Analysis of Anisotropic Damage in Brittle Materials

Pensée, Vincent; Kondo, Djimédo; Dormieux, Luc

doi:10.1061/(asce)0733-9399(2002)128:8(889)

Cited by 200 publications

(112 citation statements)

References 23 publications

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“…Previous studies (e.g. [24]) have shown that no significant difference in accuracy is obtained if 33 crack families are used rather than 21. The set of 21 families of microcracks are retained in the present work.…”

Section: Damage Modeling Accounting For Unilateral Effects In Presencmentioning

confidence: 93%

“…Therefore, the implementation of the anisotropic damage model requires an orientational average (integration) over the surface of unit sphere. This numerical implementation procedure is inspired from studies on microplane models [3] (see also [24] in the context of micromechanical damage models).…”

Section: Damage Modeling Accounting For Unilateral Effects In Presencmentioning

confidence: 99%

“…Modeling of such behavior is generally performed by considering purely macroscopic or micromechanically-based damage models (see for instance [1,9,21,12], etc.). Recent developments in homogenization of microcracked media provides now physical and mathematical models for the description of damage-induced anisotropy, as well as cracks closure effects ( [23,24,7]). The above models have been applied for geomaterials including concrete or rock-like media [27].…”

Section: Introductionmentioning

confidence: 99%

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A two scale anisotropic damage model accounting for initial stresses in microcracked materials

Levasseur

Collin

Charlier

et al. 2011

Engineering Fracture Mechanics

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a b s t r a c tIn a recent study [15], we proposed a class of isotropic damage models which account for initial stresses. The present paper extends this approach to anisotropic damage due to growth of an arbitrarily penny-shaped microcracks system. The basic principle of the upscaling technique in the presence of initial stress is first recalled. Then, we derive a closed-form expression of the elastic energy potential corresponding to a system of arbitrarily oriented microcracks. It is shown that the coupling between initial stresses and damage is strongly dependent of the microcracks density and orientation. Predictions of the proposed model are illustrated through the investigation of the influence of initial stresses on the material response under non monotonous loading paths. Finally, by considering a particular distribution of microcracks orientation, described by a second order damage tensor, it is shown that the model is a generalization of the macroscopic damage model of Halm and Dragon [9], for which a physically-based interpretation is then proposed.

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Section: Damage Modeling Accounting For Unilateral Effects In Presencmentioning

confidence: 93%

Section: Damage Modeling Accounting For Unilateral Effects In Presencmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A two scale anisotropic damage model accounting for initial stresses in microcracked materials

Levasseur

Collin

Charlier

et al. 2011

Engineering Fracture Mechanics

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“…The formulae of the "Appendix" are based on so-called Mori-Tanaka homogenization schemes [23], where the mechanical interactions between inhomogeneities (here viscous interfaces) in a homogeneous matrix are considered not up to complete detail, but rather in an average sense, see, e.g., [1,2,24] for more detailed discussions: each interface (or more generally, each inhomogeneity) is formally embedded in a fictitious matrix undergoing the mean strains of the actual material matrix, these strains being different from the macroscopic strains acting on the entire RVE; the matrix and inhomogeneity strains are enforced to fulfill the strain average rule for the entire RVE. The Mori-Tanaka scheme has been repeatedly used for modeling the behavior of cracked materials [25][26][27]. In particular, it has been shown that in the case of sharp cracks (exhibiting the same morphology as the interfaces), the aforementioned average consideration of inhomogeneity interaction leads to remarkably precise results for the overall homogenized stiffness properties, when compared to solutions accounting for fully explicit interactions, as has been shown by Kachanov et al [25].…”

Section: State Equations For Uniform Strain Boundary Conditionsmentioning

confidence: 94%

How interface size, density, and viscosity affect creep and relaxation functions of matrix-interface composites: a micromechanical study

2015

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Matrix-inclusion composites are known to exhibit interaction among the inclusions. When it comes to the special case of inclusions in form of flat interfaces, interaction among interfaces would be clearly expected, but the two-dimensional nature of interfaces implies quite surprising interaction properties. This is the motivation to analyze how interaction among two different classes of microscopic interfaces manifests itself in macroscopic creep and relaxation functions of matrix-interface composites. To this end, we analyze composites made of a linear elastic solid matrix hosting parallel interfaces, and we consider that creep and relaxation of such composites result from micro-sliding within adsorbed fluid layers filling the interfaces. The latter idea was recently elaborated in the framework of continuum micromechanics, exploiting eigenstress homogenization schemes, see Shahidi et al. (Eur J Mech A Solids 45:41-58, 2014). After a rather simple mathematical exercise, it becomes obvious that creep functions do not reflect any interface interaction. Mathematical derivation of relaxation functions, however, turns out to be much more challenging because of pronounced interface interaction. Based on a careful selection of solution methods, including Laplace transforms and the method of non-dimensionalization, we analytically derive a closed-form expression of the relaxation functions, which provides the sought insight into interface interaction. The seeming paradox that no interface interaction can be identified from creep functions, while interface interaction manifests itself very clearly in the relaxation functions of matrix-interface materials, is finally resolved based on stress and strain average rules for interfaced composites. They clarify that uniform stress boundary conditions lead to a direct external control of average stress and strain states in the solid matrix, and this prevents interaction among interfaces. Under uniform strain boundary conditions, in turn, interfacial dislocations do influence the average stress and strain states in the solid matrix, and this results in pronounced interface interaction.

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“…(32) motivates us to assume that the damage dissipation also evolves independently on each orientation, thus identifying U X as the thermodynamic force conjugate to d X . It should be noted that this basic assumption overlaps with certain concepts in which multiple-plane representations of inelasticity are derived (SEAMAN and DEIN, 1983;BAZˇANT and GAMBAROVA, 1984;JU and LEE, 1991a,b;ESPINOSA and BRAR, 1995;PENSE´E et al, 2002).…”

Section: Dissipation and Internal State Variablesmentioning

confidence: 89%

Orientation-based Continuum Damage Models for Rocks

Liu¹,

Yin²,

Liang³

Pageoph Topical Volumes

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Abstract-A general formulation of the Helmholtz free energy used in thermodynamics of damage process of rocks is derived within a multi-scale framework. Such a physically-based thermodynamic state potential has a hybrid, discrete/continuum, nature in the sense that it adopts a continuum description but subsumes the statistical ensemble average of the action of the entirety of microscopic degrees of freedom. The choice of the relevant damage variables results therefore directly from the breaking of contact cohesive bonds, and it naturally obeys the Clausius-Duhem inequality. Furthermore, motivated by the fact that the free energy is formulated by the integral of potentials independently defined on different orientations over the upper hemisphere, the damage evolution equation is formulated on a generic orientation. Consequently, the mechanical behavior of a rock material generally becomes anisotropic characteristics in the inelastic regime even if the material is initially isotropic, thus introducing dissipation-induced anisotropy in a very natural and simple way. Finally, the development of the lattice solid model can be cast into the framework of the orientation based continuum constitutive model.

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Micromechanical Analysis of Anisotropic Damage in Brittle Materials

Cited by 200 publications

References 23 publications

A two scale anisotropic damage model accounting for initial stresses in microcracked materials

A two scale anisotropic damage model accounting for initial stresses in microcracked materials

How interface size, density, and viscosity affect creep and relaxation functions of matrix-interface composites: a micromechanical study

Orientation-based Continuum Damage Models for Rocks

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