Damage tensors and the crack density distribution

Lubarda, Vlado A.; Krajčinović, Dušan

doi:10.1016/0020-7683(93)90158-4

Cited by 270 publications

(107 citation statements)

References 17 publications

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“…n; respectively; and E 0 and n 0 are, respectively, Young's modulus and Poisson's ratio of the undamaged material. In order to define a state variable of anisotropic damage in the framework of macroscopic modelling, tensorial representation methods are widely used for the approximation of crack distribution [13][14][15][33][34][35]. In the present work, the approximation with a second-order tensor is chosen as it is the simplest choice.…”

Section: Anisotropic Damage Modelmentioning

confidence: 99%

“…By using the definition given in (3), according to the previous works by Lubarda and Krajcinovic [35], Yang et al [36] and Pensee et al [32], the continuous crack density function oð ! nÞ can be expressed as a function of the macroscopic damage tensor D: Therefore, for the two particular cases corresponding to solids containing fully opened and closed cracks, the macroscopic free enthalpy (1) can be analytically integrated and expressed as a function of the damage tensor D:…”

Section: Anisotropic Damage Modelmentioning

confidence: 99%

See 1 more Smart Citation

Coupling between anisotropic damage and permeability variation in brittle rocks

Shao

Zhou

Chau

2005

Int. J. Numer. Anal. Meth. Geomech.

150

117

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SUMMARYIn this paper, a coupled constitutive model is proposed for anisotropic damage and permeability variation in brittle rocks under deviatoric compressive stresses. The formulation of the model is based on experimental evidences and main physical mechanisms involved in the scale of microcracks are taken into account. The proposed model is expressed in the macroscopic framework and can be easily implemented for engineering application. The macroscopic free enthalpy of cracked solid is first determined by approximating crack distribution by a second-order damage tensor. The effective elastic properties of damaged material are then derived from the free enthalpy function. The damage evolution is related to the crack growth in multiple orientations. A pragmatic approach inspired from fracture mechanics is used for the formulation of the crack propagation criterion. Compressive stress induced crack opening is taken into account and leads to macroscopic volumetric dilatancy and permeability variation. The overall permeability tensor of cracked material is determined using a micro-macro averaging procedure. Darcy's law is used for fluid flow at the macroscopic scale whereas laminar flow is assumed at the microcrack scale. Hydraulic connectivity of cracks increases with crack growth. The proposed model is applied to the Lac du Bonnet granite. Generally, good agreement is observed between numerical simulations and experimental data.

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Section: Anisotropic Damage Modelmentioning

confidence: 99%

Section: Anisotropic Damage Modelmentioning

confidence: 99%

Coupling between anisotropic damage and permeability variation in brittle rocks

Shao

Zhou

Chau

2005

Int. J. Numer. Anal. Meth. Geomech.

150

117

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“…For this, we take advantage of approximations already used by Lubarda and Krajcinovic [17] (see also Thikhomirov et al [26], Qiang et al [25] and Pensée [22]). …”

Section: Approximate Anisotropic Damage Model In Presence Of Initial mentioning

confidence: 99%

“…Following [17], the continuous distribution of microcracks density parameter, denoted here d(n), can be described by a second order tensor q such as d(n) = q:(n n). Vector n represents the unit normal to a considered microcracks family.…”

Section: Anisotropic Damage Representation By Means Of a Second Ordermentioning

confidence: 99%

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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“…Voyiadjis and Kattan (2007) related continuum damage mechanics of metals with the concept of fabric tensors. They applied the concept of fabric tensors introduced by Kanatani (1984) and further elaborated upon by Lubarda and Krajcinovic (1993) as well as the work of Zysset and Curnier (1995) and Cauvin and Testa (1999) into the formulation of an elasticity tensor of damaged metallic material. The proposed work is an extension of the work of Voyiadjis and Kattan (2007) to incorporate the fabric tensors in the study of damage mechanics of composite materials.…”

Section: Introductionmentioning

confidence: 99%