On a Flat Ellipsoidal Inclusion or Crack in Three-Dimensional Anisotropic Media

Huang, Jin H.; Liu, Hsien‐Kuang

doi:10.1016/s0020-7225(97)00046-3

Cited by 20 publications

(11 citation statements)

References 9 publications

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“…Using in (40) the parametrization ξ = √ 1 − z 2 (cos φ l i + sin φ m i ) + z n i and dS ξ = dz dφ as well as an analogy with a result obtained in the framework of elasticity in Huang and Liu (1998), / i hom writes:…”

Section: Influence Of the Normal Component Of The Fracture Permeabilitymentioning

confidence: 99%

Effective Permeability of Media with a Dense Network of Long and Micro Fractures

Barthélémy

2008

Transp Porous Med

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This article presents a new methodology to estimate the effective permeability of random fractured media of any anisotropy containing both microfractures and a large number of long fractures crosscutting the representative volume element. The fractures are replaced by fictitious permeable materials for which the tangential permeability is deduced from a Poiseuille flow. A self-consistent scheme is proposed to derive the macroscopic permeability. On the one hand, the contribution of long fractures to the effective permeability writes by simple superposition of the fracture tangential permeabilities. On the other hand, the contribution of microfractures needs to resort to auxiliary problems requiring the computation of second-order Hill (or Eshelby) tensors related to ellipsoids embedded in an anisotropic matrix, for which a complete procedure is detailed. The effect of the microfracture normal permeability is put in evidence in the upscaling scheme and analyzed. In particular, it is shown that it must be chosen large enough to allow the connections between families. Examples are finally developed and compared to numerical simulations in the 2D case.Keywords Anisotropic effective permeability · Self-consistent scheme · Fracture permeability · Double scale fracture network Nomenclature XVector notation 7 Second-order tensor notation p Pressure field ∇ P Macroscopic pressure gradient qMicroscopic filtration vector Q Macroscopic filtration vector µ Fluid viscosity

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Section: Influence Of the Normal Component Of The Fracture Permeabilitymentioning

confidence: 99%

Effective Permeability of Media with a Dense Network of Long and Micro Fractures

Barthélémy

2008

Transp Porous Med

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“…where is the stress disturbance resulting from the crack. This stress disturbance can be simulated by the eigenstress derived from an equivalent ellipsoidal inclusion with eigenstrain * as [7].…”

Section: The Rupture Stressmentioning

confidence: 99%

Rupture stress of eutectic composite ceramics with rod-shaped crystals

Yu¹,

Ni²,

Liu³

et al. 2018

Vib. proced.

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Eutectic composite ceramics has a wide range of applications in the aerospace industry due to its excellent mechanical properties. The rupture stress of the materials is a subject of considerable importance. Eutectic composite ceramics primarily consist of rod-shaped crystals, with a small amount of particles and preexisting defects dispersed throughout. Aligned nano-micron fibers are embedded within the rod-shaped crystals. Rupture stress of a eutectic composite ceramic depends on its fracture surface energy and preexisting defects. In this study, the equivalent fracture surface energy of a eutectic ceramic composite was calculated based on its additional fracture work. Next, the effects of the preexisting defects were considered. Then, a micromechanical model of the eutectic composite ceramic was established based on its microstructural characteristics. The defects were assumed to be lamellar, and the surrounding matrix was assumed to be transversely isotropic. Using this information, the rupture stress of the eutectic ceramic composite was predicted. A comparison of the theoretical and experimental results indicated that the predicted rupture stresses corresponded with the tested data.

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“…Another expression of P, coming from an integration by parts of the first integral of (9), can be found in Huang and Liu (1998) …”

Section: D Crack Modelmentioning

confidence: 99%

“…The computation requires a Taylor expansion of the Hill tensor up to the first order with respect to the aspect ratio. A procedure similar to that of Masson (2008) is implemented to compute the first order of this expansion also appearing as a double integral (Huang and Liu, 1998). The solution of Gruescu et al (2005) in 2D is retrieved and extended to the full anisotropic 3D case.…”

Section: Introductionmentioning

confidence: 99%

Compliance and Hill polarization tensor of a crack in an anisotropic matrix

Barthélémy¹

2009

International Journal of Solids and Structures

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a b s t r a c tThis work aims at developing an efficient method to compute the compliance due to a crack modeled as a flat ellipsoid of any shape in an infinite elastic matrix of arbitrary anisotropy (Eshelby problem) when no closed-form solution seems currently available. Whereas the solution of this problem usually requires the calculation of the so-called fourth-order Hill polarization tensor if the ellipsoid is not singular, it is shown that the crack compliance can be derived from the first-order term in the Taylor expansion of the Hill tensor with respect to the smallest aspect ratio of the ellipsoidal inclusion. For a 3D ellipsoidal crack model, this first-order term is expressed as a simple integral thanks to the Cauchy residue theorem. A similar method allows to express the same term in the case of a cylindrical crack model without any integral. A numerical example is finally treated.

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On a Flat Ellipsoidal Inclusion or Crack in Three-Dimensional Anisotropic Media

Cited by 20 publications

References 9 publications

Effective Permeability of Media with a Dense Network of Long and Micro Fractures

Effective Permeability of Media with a Dense Network of Long and Micro Fractures

Rupture stress of eutectic composite ceramics with rod-shaped crystals

Compliance and Hill polarization tensor of a crack in an anisotropic matrix

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