Characterization of anisotropy in porous media by means of linear intercept measurements

Inglis, Dean; Pietruszczak, S.

doi:10.1016/s0020-7683(02)00595-4

Cited by 54 publications

(34 citation statements)

References 20 publications

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“…A similar observation had earlier been made in granular materials for the three-dimensional distribution of grain contact normals [15,19]. The representation of the ellipsoid based on mean intercept length as a second rank tensor, the fabric tensor H, was proposed in [9,11]. The fabric tensor approach has also been used in soil mechanics [14], and microstructural measures other than the mean intercept length such as the volume orientation distribution [16], star-volume distribution [7], or the star-length distribution [17] have been used.…”

Section: Introductionsupporting

confidence: 57%

Fabric tensor based boundary element analysis of porous solids

Berger

2011

Engineering Analysis with Boundary Elements

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Section: Introductionsupporting

confidence: 57%

Fabric tensor based boundary element analysis of porous solids

Berger

2011

Engineering Analysis with Boundary Elements

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“…For scalar Minkowski functionals, however, the value is just a single real-valued number and for tensorial Minkowski functionals it is a tensor, here specifi cally a symmetric rank-two tensor with six independent real-valued components. Other examples of tensorial shape indices of rank two defi ned for a body K are the tensor of inertia I , [ 68 ] the mean intercept length tensor MIL ( K ), [69][70][71][72][73][74][75] see also Ref. [76], and the quadrupole tensor Q , [ 77 ] see also Ref.…”

Section: Minkowski Tensorsmentioning

confidence: 99%

Minkowski Tensor Shape Analysis of Cellular, Granular and Porous Structures

et al. 2011

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Predicting physical properties of materials with spatially complex structures is one of the most challenging problems in material science. One key to a better understanding of such materials is the geometric characterization of their spatial structure. Minkowski tensors are tensorial shape indices that allow quantitative characterization of the anisotropy of complex materials and are particularly well suited for developing structure-property relationships for tensor-valued or orientation-dependent physical properties. They are fundamental shape indices, in some sense being the simplest generalization of the concepts of volume, surface and integral curvatures to tensor-valued quantities. Minkowski tensors are based on a solid mathematical foundation provided by integral and stochastic geometry, and are endowed with strong robustness and completeness theorems. The versatile definition of Minkowski tensors applies widely to different types of morphologies, including ordered and disordered structures. Fast linear-time algorithms are available for their computation. This article provides a practical overview of the different uses of Minkowski tensors to extract quantitative physically-relevant spatial structure information from experimental and simulated data, both in 2D and 3D. Applications are presented that quantify (a) alignment of co-polymer films by an electric field imaged by surface force microscopy; (b) local cell anisotropy of spherical bead pack models for granular matter and of closed-cell liquid foam models; (c) surface orientation in open-cell solid foams studied by X-ray tomography; and (d) defect densities and locations in molecular dynamics simulations of crystalline copper.

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“…In order to define the principal directions of permeability a measure of material microstructure is required. Since the hydraulic properties depend on both the size and the distribution of void space, the specific descriptor adopted here is the "areal pore size" ρ A , which is analogous to that introduced in earlier work by Pietruszczak and Krucinski [10] and Inglis and Pietruszczak [5]. The definition is based on principles of stereology and employs linear intercept measurements.…”

Section: Hydraulic Properties; Darcy's Law For Anisotropic Porous Matmentioning

confidence: 99%

Description of hydraulic and strength properties of anisotropic geomaterials

Pietruszczak¹,

Pande²

2012

Studia Geotechnica Et Mechanica

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Abstract:In this paper, a simple generalization of Darcy's law is proposed for the description of hydraulic properties of anisotropic porous materials. The coefficient of permeability is defined as a scalarvalued function of orientation. The principal directions of permeability are determined from a fabric descriptor specifying the distribution of average pore size. An example is provided for identification of material parameters, which is based on an idealized "pipe network model". A procedure for defining the anisotropy in strength properties, which incorporates a conceptually similar approach, is also reviewed and an illustrative example is provided.

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Characterization of anisotropy in porous media by means of linear intercept measurements

Cited by 54 publications

References 20 publications

Fabric tensor based boundary element analysis of porous solids

Fabric tensor based boundary element analysis of porous solids

Minkowski Tensor Shape Analysis of Cellular, Granular and Porous Structures

Description of hydraulic and strength properties of anisotropic geomaterials

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