The sliding crack model of brittle deformation: An internal variable approach

Basista, Michał; Groß, Dietmar

doi:10.1016/s0020-7683(97)00031-0

Cited by 111 publications

(58 citation statements)

References 34 publications

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“…The second step is to propose a suitable damage evolution law for microcrack growth. This damage evolution law can be obtained using fracture mechanics consideration via crack propagation criteria [7][8][9][10], and thermodynamic considerations via a damage dissipation potential [3,11,12]. The main features related to microcrack growth, opening and closure, friction, interaction between cracks, could be taken into account in such micromechanical models.…”

Section: Introductionmentioning

confidence: 99%

Modelling of anisotropic damage in brittle rocks under compression dominated stresses

Shao

2002

Num Anal Meth Geomechanics

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SUMMARYA new model for describing induced anisotropic damage in brittle rocks is proposed. Although phenomenological, the model is based on physical grounds of micromechanical analysis. Induced damage is represented by a second rank tensor, which is related to the density and orientation of microcracks. Damage evolution is related to the propagation condition of microcracks. The onset of microcrack coalescence leading to softening behaviour is also considered. The effective elastic compliance of the damaged material is obtained from a specific form of Gibbs potential. Irreversible damage-related strains due to residual opening of microcracks after unloading are also captured. All the model's parameters could be determined from conventional triaxial compression tests. The proposed model is applied to a typical brittle rock. Comparison between test data and numerical simulations shows an overall good agreement. The proposed model is able to describe the main features related to induced microcracks in brittle geomaterials.

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Section: Introductionmentioning

confidence: 99%

Modelling of anisotropic damage in brittle rocks under compression dominated stresses

Shao

2002

Num Anal Meth Geomechanics

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“…During the loading process the rates of crack slidingḃ and extensionl are obtained with reference to two limit states corresponding to sliding and damage activation (Moss and Gupta, 1982;Basista and Gross, 1998), under the constraints provided by the unilateral contact condition between the opposite faces of the wing cracks (that implies b n 0) and the irreversibility condition of crack evolution (l 0). Since crack sliding and growth increments may be expressed in terms of the stress ratesσ , the right side of equation (6) states the constitutive equation by means of the incremental fourth-order compliance tensor D i t (ϑ n ).…”

Section: Incremental Constitutive Response Of Uniaxially Compressed Bmentioning

confidence: 99%

“…Since crack sliding and growth increments may be expressed in terms of the stress ratesσ , the right side of equation (6) states the constitutive equation by means of the incremental fourth-order compliance tensor D i t (ϑ n ). Complex forms for D i t (ϑ n ) have been derived at different levels of detail by Moss and Gupta (1982), Nemat-Nasser and Obata (1988) and more recently by Basista and Gross (1998). On the other hand, the mentioned formulations are referred to principal stress states in order to describe the dilatancy of brittle materials induced by crack growth aligned with the dominant compression; yet, general formulations extending the model response to shearing stresses, as required by the stability analysis, do not seem to be available.…”

Section: Incremental Constitutive Response Of Uniaxially Compressed Bmentioning

confidence: 99%

“…Thus, the overall instantaneous stiffness tensor C * = D * −1 can be obtained. It is interesting to point out that D * differs from the instantaneous compliance tensor by Basista and Gross (1998), who discussed two alternative simplified crack configurations consisting either of a single crack of length 2l n or of two noninteracting cracks like the ones in Figs 1c, depending on the parameter chosen to drive the loading process. In the second case the formulation leads to the same results by equation (15) at the onset of crack propagation when the size of the wing cracks is much smaller than that of the initial flaw.…”

Section: Incremental Constitutive Response Of Uniaxially Compressed Bmentioning

confidence: 99%

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Uniaxial compressive failure of brittle materials as instability of damaging microcracked solids

Gambarotta

Monetto

2002

European Journal of Mechanics - A/Solids

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Uniaxial compressive failure of brittle materials is modelled as buckling of microcracked solids undergoing damage. The brittle material is modelled as an isotropic linear elastic matrix containing a random distribution of non-interacting microcracks. Increasing the stress level, the material response evolves from isotropy at the natural state to orthotropy in damaged states. Furthermore, the overall stiffness decreases until a critical condition of equilibrium bifurcation may be reached. The related critical value of the compressive stress, provided by the buckling analysis of orthotropic elastic sheets, is then assumed as compressive strength of the brittle material. In order to predict damage evolution and model the incremental response, simplified crack configurations are considered. The obtained theoretical results show the dependence of the compressive strength on the matrix toughness and microcrack parameters, and are in good correlation with the experimental results obtained on compressed specimens constrained between frictionless devices.  2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.

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“…Nemat-Nasser and Hori 1999; Andrieux et al 1986;Prat and Bazant 1997;Caiazzo and Constanzo 2000;Pensée et al 2002;Lene 2004;Basista and Gross 1989;Li et al 2004;Raghavan and Ghosh C. Dascalu (B) · G. Bilbie Laboratoire 3S-R, UJF, INPG, CNRS UMR 5221, BP 53, 38041 Grenoble cedex 9, France e-mail: cristian.dascalu@hmg.inpg.fr 2005). In parallel with these developments, the material or configurational mechanics (e.g.…”

Section: Introductionmentioning

confidence: 99%

A multiscale approach to damage configurational forces

Dascalu

Bilbie

2007

Int J Fract

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A two-scale homogenization method is used to construct a damage model in the framework of configurational mechanics. The upscaling procedure allows for the identification of damage configurational forces as the result of the microscopic fracture analysis. The obtained damage equation incorporates stiffness degradation, material softening, unilaterality, induced anisotropy. The balance of configurational forces naturally captures a microscopic length, leading to size effects in the overall damage response. The new approach is illustrated in the case of brittle damage, for a three point bending test. Extended finite elements are used for the numerical modeling of macro-crack initiation and growth. The influence of the microscopic size on the failure initiation stress is analyzed and it is shown that this dependence follows a Hall-Petch type rule.

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The sliding crack model of brittle deformation: An internal variable approach

Cited by 111 publications

References 34 publications

Modelling of anisotropic damage in brittle rocks under compression dominated stresses

Modelling of anisotropic damage in brittle rocks under compression dominated stresses

Uniaxial compressive failure of brittle materials as instability of damaging microcracked solids

A multiscale approach to damage configurational forces

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