A probabilistic nonlocal model for crack initiation and propagation in heterogeneous brittle materials

Guy, Nicolas; Seyedi, Darius; Hild, François

doi:10.1002/nme.3362

Cited by 16 publications

(13 citation statements)

References 36 publications

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“…It has been shown in Guy et al (2012) that, for a specific range of material length scale and crack length over a domain, the material length scale itself can be used as scale parameter of the Weibull distribution. In our work, the material length scale is accounted in the generation of the hypothetical sample used successively to generate the shape and scale parameters by means of the MLE method.…”

Section: Stochastic Approachmentioning

confidence: 99%

Experimental Study and Numerical Modeling of Fracture Propagation in Shale Rocks During Brazilian Disk Test

et al. 2018

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Reliable prediction of fracture process in shale-gas rocks remains one of the most significant challenges for establishing sustained economic oil and gas production. This paper presents a modeling framework for simulation of crack propagation in heterogeneous shale rocks. The framework is on the basis of a variational approach, consistent with Griffith's theory. The modeling framework is used to reproduce the fracture propagation process in shale rock samples under standard Brazilian disk test conditions. Data collected from the experiments are employed to determine the testing specimens' tensile strength and fracture toughness. To incorporate the effects of shale formation heterogeneity in the simulation of crack paths, fracture properties of the specimens are defined as spatially random fields. A computational strategy on the basis of stochastic finite element theory is developed that allows to incorporate the effects of heterogeneity of shale rocks on the fracture evolution. A parametric study has been carried out to better understand how anisotropy and heterogeneity of the mechanical properties affect both direction of cracks and rock strength.

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Section: Stochastic Approachmentioning

confidence: 99%

Experimental Study and Numerical Modeling of Fracture Propagation in Shale Rocks During Brazilian Disk Test

et al. 2018

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“…a flaw density of 1×10 −9 m −3 in a cell that is only 0.1 mm on a side). Such a situation is outside of the domain that the model was designed for, but the model could be augmented by introducing a non-local approach similar to the one used by [16]. The development of such a model is beyond the scope of this paper.…”

Section: Implementation Of Materials Variabilitymentioning

confidence: 99%

Multi-scale defect interactions in high-rate failure of brittle materials, Part II: Application to design of protection materials

Tonge

Ramesh

2016

Journal of the Mechanics and Physics of Solids

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Micromechanics based damage models, such as the model presented in part I of this 2 part series [1], have the potential to suggest promising directions for materials design. However, to reach their full potential these models must demonstrate that they capture the relevant physical processes. In this work, we apply the multiscale material model described in [1] to ballistic impacts on the advanced ceramic boron carbide and suggest possible directions for improving the performance of boron carbide under impact conditions. We simulate both dynamic uniaxial compression and simplified ballistic loading geometries to demonstrate that the material model captures the relevant physics in these problems and to interrogate the sensitivity of the simulation results to some of the model input parameters. Under dynamic compression, we show that the simulated peak strength is sensitive to the maximum crack growth velocity and the flaw distribution, while the stress collapse portion of the test is partially influenced by the granular flow behavior of the fully damaged material. From simulations of simplified ballistic impact, we suggest that the total amount of granular flow (a possible performance metric) can be reduced by either a larger granular flow slope (more angular fragments) or a larger granular flow timescale (larger fragments). We then discuss the implications for materials design.

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“…Two principal categories exist : one consists in the enrichment of the constitutive law with for instance non-local approaches (Bazant et al, 1984;Pijaudier-Cabot & Bazant, 1987;Peerlings et al, 1996b;Guy et al, 2012) or gradient plasticity (Aifantis, 265 1984;de Borst & Mühlhaus, 1992;Peerlings et al, 1996a), the other one consists in the enrichment of the continuum kinematics with microstructure effects. For this second category the microkinematics are characterised at microscale in addition to the classical macrokinematics (Cosserat & Cosserat, 1909;Toupin, 1962;Mindlin, 1964;Germain, 1973).…”

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confidence: 99%

Shear banding modelling in cross-anisotropic rocks

Pardoen

Seyedi²,

Collin

2015

International Journal of Solids and Structures

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Sedimentary geomaterials such as rocks frequently exhibit cross-anisotropic properties and their behaviour depends on the direction of loading with respect to their microstructure. As far as material rupture is concerned, localised deformation in shear band mode appears generally before cracks and material failure. cavation fractured zone that develops around a gallery is strongly influenced by the material anisotropy.

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A probabilistic nonlocal model for crack initiation and propagation in heterogeneous brittle materials

Cited by 16 publications

References 36 publications

Experimental Study and Numerical Modeling of Fracture Propagation in Shale Rocks During Brazilian Disk Test

Experimental Study and Numerical Modeling of Fracture Propagation in Shale Rocks During Brazilian Disk Test

Multi-scale defect interactions in high-rate failure of brittle materials, Part II: Application to design of protection materials

Shear banding modelling in cross-anisotropic rocks

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