On micromechanical modeling of orthotropic solids with parallel cracks

Vasylevskyi, Kostiantyn; Drach, Borys; Tsukrov, Igor

doi:10.1016/j.ijsolstr.2018.02.038

Cited by 8 publications

(14 citation statements)

References 42 publications

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“…Consistency of the geometrical representation of the cracks was ensured by comparing different shapes with small aspect ratios, and the representativeness of the simulation box was investigated. The results show that both out-of-plane effective elastic moduli are very well predicted by the differential scheme, which confirms previous results of the literature (Dahm and Becker [7], Orlowsky et al [23], Shen and Li [27], Vasylevskyi et al [28]). A new interesting result obtained in the present study is that this scheme is also very good at predicting the average crack opening.…”

Section: Discussionsupporting

confidence: 90%

“…It makes use of the python tool Combs developed in the framework of the CAD platform Salome 1 . In the present paper, following Charpin and Ehrlacher [6] and Vasylevskyi et al [28], it was decided to introduce cracks with a shape approaching the one considered in the analytical developments, i.e. with a non-zero volume, and to further avoid a possible crack interpenetration by imposing a minimal distance (1/100 of the box edge dimension) between cracks, although overlapping is technically possible with Salome.…”

Section: Preliminary Investigationsmentioning

confidence: 99%

“…To limit the mesh size, the number of cracks was restrained in the range 30 to 60, corresponding to a crack density parameter varying from 0.2 to 0.8. With the available numerical tools, it is possible to generate geometries with crack aspect ratios as low as 1/1000, to be compared with 1/100 in Vasylevskyi et al [28]. As a consequence, the numerical strain/stress fields within the cracks are probably questionable due to elements whose shape is not well suited for FE simulations.…”

Section: Preliminary Investigationsmentioning

confidence: 99%

“…The authors concluded that the FRIDD method was good at estimating the poromechanical properties of cracked media, but it should be noted that the presented results did not include the differential estimate. Finally, the most recent results are due to Vasylevskyi et al [28], who performed 3D finite element calculations on 3D periodic cells of ellipsoids with an aspect ratio of 0.01 embedded in an orthotropic matrix. Here, the authors identified the differential scheme as giving the best results for out-of-plane moduli, and the Mori-Tanaka scheme for the in-plane ones.…”

Section: Introductionmentioning

confidence: 99%

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Closure of parallel cracks: Micromechanical estimates versus finite element computations

Bluthé

Bary

Lemarchand

2020

European Journal of Mechanics - A/Solids

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3D finite element simulations have been performed in order to assess the ability of four classical homogenization schemes to model the elastic behavior of solids with parallel cracks, namely the dilute, Mori-Tanaka, self-consistent and differential schemes. The cracks have been represented by right circular cylinders with aspect ratios as low as 10 −3 in the simulations whose centroids are randomly located in the REV. Special attention has been paid to the crack aspect ratio variation predicted by the different schemes, since the goal is ultimately to propose a non-linear micromechanical model of a cracked solid, taking complete crack closure into account.The results confirm earlier studies which showed that the differential scheme was best suited for this kind of morphology when computing elastic moduli, but additionally, we show that changes in crack aperture are also accurately predicted. It is however noted that the randomness in the positions of the cracks leads to significant scatter in the magnitude of the aperture variation inside a given simulation, which suggests that the cracks do not close simultaneously. As a consequence, nonlinear numerical simulations accounting for contact between the crack lips should be performed in order to completely validate a non-linear micromechanical model in alternate tension/compression loading cases.

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Section: Discussionsupporting

confidence: 90%

Section: Preliminary Investigationsmentioning

confidence: 99%

Section: Preliminary Investigationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Closure of parallel cracks: Micromechanical estimates versus finite element computations

Bluthé

Bary

Lemarchand

2020

European Journal of Mechanics - A/Solids

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“…Comparison of shear modulus to the crack density for sphere‐equivalency method (red line), NIA approximation method (green line), Hudson method (blue line), and Eshelby‐Cheng method (orange line). The finite‐element results are from Vasylevskyi et al (2018). …”

Section: Discussionmentioning

confidence: 99%

Crack‐Induced Shear‐Wave Orthorhombic Anisotropy: Modeling and Inversion of Shear‐Wave Borehole Measurements

Tang

et al. 2020

JGR Solid Earth

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Rocks in horizontally layered sediments often exhibit transversely isotropic (TI) characteristics and contain aligned fractures/cracks due to tectonic movement and stress. We model the effective elastic properties of the TI medium containing vertically aligned cracks using the sphere‐equivalency of the effective scattering method. Results show that the corresponding anisotropy of the VTI background medium containing vertically fluid‐filled ellipsoidal inclusions can be characterized by the orthorhombic anisotropy model. The shear‐wave anisotropy of the model is governed by three anisotropy parameters, corresponding to the horizontal plane, and the two vertical planes that are normal and parallel to the crack plane, respectively. Effects on anisotropy parameters due to cracks are examined in detail, showing that one can use shear‐wave measurements to evaluate both the TI and crack parameters of the cracked TI‐rock. Based on the theoretical analysis, we develop an inversion method to estimate shear anisotropy parameters from the four‐component shear‐wave logging measurement in a vertical borehole penetrating the orthorhombic rock. The inversion method is validated with synthetic data and applied to interpret acoustic anisotropy from borehole measurements acquired in a fractured shale formation, where theoretical predictions and measurements are found in good agreement.

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Contribution of FE and FFT-based methods to the determination of the effective elastic and conduction properties of composite media with flat inclusions and infinite contrast

Bluthé

Bary

Lemarchand

2021

International Journal of Solids and Structures

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On micromechanical modeling of orthotropic solids with parallel cracks

Cited by 8 publications

References 42 publications

Closure of parallel cracks: Micromechanical estimates versus finite element computations

Closure of parallel cracks: Micromechanical estimates versus finite element computations

Crack‐Induced Shear‐Wave Orthorhombic Anisotropy: Modeling and Inversion of Shear‐Wave Borehole Measurements

Contribution of FE and FFT-based methods to the determination of the effective elastic and conduction properties of composite media with flat inclusions and infinite contrast

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