Fiber Orientation Distribution Functions and Orientation Tensors for Different Material Symmetries

Moakher, Maher; Basser, Peter J.

doi:10.1007/978-3-319-15090-1_3

Cited by 9 publications

(9 citation statements)

References 29 publications

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“…The present work follows the suggestion of describing the fiber orientation state with tensors of the first kind [1,37]. In general, the n th -order orientation tensor N n (x, t) of the first kind can be written as follows [1,37,44]:…”

Section: Orientation Tensorsmentioning

confidence: 99%

“…Based on (14) and (15) the following statements can be made. In case of isotropic fiber orientation states N iso = I/3 and N iso = P 1 /3 + 2P 2 /15 [6,44], the trace of σ V is equal to tr(σ V ) = 0, and p describes the hydrostatic stress state completely. Conversely, anisotropic fiber orientation states yield tr(…”

Section: As a Consequence The Right Minor Symmetrymentioning

confidence: 99%

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Coupled simulation of flow-induced viscous and elastic anisotropy of short-fiber reinforced composites

2021

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The present work discusses the impact of the back coupling of the fiber orientation distribution on the base flow and on the fiber orientation itself during mold filling simulations. Flows through a channel and over a backward-facing step are investigated. Different closure approximations are considered for modeling the flow-induced evolution of anisotropy. The results corresponding to the decoupled approach, in which the effect of fibers on local fluid properties is neglected, build the basis of comparison. The modeling is limited to a laminar, incompressible, and isothermal flow of a fiber suspension consisting of rigid short fibers suspended in an isotropic Newtonian matrix fluid. A linear, anisotropic constitutive law is used in combination with a uniform fiber volume fraction of 10% and an aspect ratio of 10. To evaluate the impact of back coupling and of different closure methods in view of the manufactured solid composite the resulting anisotropic elastic properties are investigated based on the Mori–Tanaka method combined with an orientation average scheme. Relative to the range [0, 1] the pointwise difference in fiber orientation between the decoupled and the coupled approach is found to be $$\pm 5{\%}$$ ± 5 % in the channel and $$\pm 30{\%}$$ ± 30 % in the backward-facing step, respectively. The viscosity and the elasticity tensor show both significant flow-induced anisotropies as well as a strong dependence on closure and coupling.

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Section: Orientation Tensorsmentioning

confidence: 99%

Section: As a Consequence The Right Minor Symmetrymentioning

confidence: 99%

Coupled simulation of flow-induced viscous and elastic anisotropy of short-fiber reinforced composites

2021

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“…Countless scholars have carried out experimental studies to explore the outcome of fiber orientation impact on fibers [19]. Reported studies [20] showed the mechanical behavior of plain knitted and twill weaved fiber and revealed that a twill woven fiber ensures excellent mechanical properties as compared to the woven 0/90 mat. Woven mat fibers afford a proper equilibrium between mechanical properties, and it is the favorite form of standard fiber mats for an engineered composite product made by hand layup methods.…”

Section: State-of-the-art On Spider Web Construction and Propertymentioning

confidence: 99%

“…Fiber orientations with 0°, 90°, +45°, and/or -45° is a standard method for designing fiber orientations and is a common practice to produce composite structures. Among these, 0°/90°, +45°/−45° orientation types are frequently used, but none of them are a Nature-inspired form of orientation [20].…”

Section: State-of-the-art On Spider Web Construction and Propertymentioning

confidence: 99%

Studies on the Geometrical Design of Spider Webs for Reinforced Composite Structures

et al. 2021

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Spider silk is an astonishingly tough biomaterial that consists almost entirely of large proteins. Studying the secrets behind the high strength nature of spider webs is very challenging due to their miniature size. In spite of their complex nature, researchers have always been inspired to mimic Nature for developing new products or enhancing the performance of existing technologies. Accordingly, the spider web can be taken as a model for optimal fiber orientation for composite materials to be used in critical structural applications. In this study an attempt is made to analyze the geometrical characteristics of the web construction building units such as spirals and radials. As a measurement tool, we have used a developed MATLAB algorithm code for measuring the node to node of rings and radials angle of orientation. Spider web image samples were collected randomly from an ecological niche with black background sample collection tools. The study shows that the radial angle of orientation is 12.7 degrees with 5 mm distance for the spirals’ mesh size. The extracted geometrical numeric values from the spider web show moderately skewed statistical data. The study sheds light on spider web utilization to develop an optimized fiber orientation reinforced composite structure for constructing, for instance, shell structures, pressure vessels and fuselage cones for the aviation industry.

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“…Since we are interested in finding clusters of orientations (as opposed to directions), we use just the antipodally symmetric part of the von-Mises-Fisher kernel (cf. [6]) given by f (e 1 , µ; κ) = C f (κ)cosh(κe 1 · µ) with mean µ and concentration parameter κ. To further account for the different strengths of the votes we employ weighting of the data points by w s in the computation of the mean shift, which is in accordance with [7].…”

Section: Analysing the Local Distribution Of Votesmentioning

confidence: 99%

Steering second-order tensor voting by vote clustering

Jörgens

Smedby

Moreno

2016

2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI)

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Among the various diffusion MRI techniques, diffusion tensor imaging (DTI) is still most commonly used in clinical practice in order to investigate connectivity and fibre anatomy in the human brain. Besides its apparent advantages of a short acquisition time and noise robustness compared to other techniques, it suffers from its major weakness of assuming a single fibre model in each voxel. This constitutes a problem for DTI fibre tracking algorithms in regions with crossing fibres. Methods approaching this problem in a postprocessing step employ diffusion-like techniques to correct the directional information. We propose an extension of tensor voting in which information from voxels with a single fibre is used to infer orientation distributions in multi fibre voxels. The method is able to resolve multiple fibre orientations by clustering tensor votes instead of adding them up. Moreover, a new vote casting procedure is proposed which is appropriate even for small neighbourhoods. To account for the locality of DTI data, we use a small neighbourhood for distributing information at a time, but apply the algorithm iteratively to close larger gaps. The method shows promising results in both synthetic cases and for processing DTI-data of the human brain.Index Terms-Tensor voting, spherical clustering, DTI 1. INTRODUCTION Diffusion MRI techniques have been used to study connectivity between different regions in the human brain. Based on local diffusion profiles in the white matter, tractography methods can extract fibre paths that connect different regions.The most mature diffusion method is diffusion tensor imaging (DTI) in which anisotropy and orientation of fibres are locally modelled through second-order tensors. The main drawback of DTI is that it is unable to resolve crossings of fibres, which are not unusual in the brain. There are two strategies for addressing this issue: either by using more advanced acquisition protocols such as high angular resolution diffusion imaging (HARDI) or by performing postprocessing of DTI data. Most of the previous work has followed the first strategy. However, it is noteworthy to mention that DTI has much shorter acquisition times and is less prone to motion artifacts than HARDI, which makes DTI more appropriate for clinical use. This means that methods following the latter

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Fiber Orientation Distribution Functions and Orientation Tensors for Different Material Symmetries

Cited by 9 publications

References 29 publications

Coupled simulation of flow-induced viscous and elastic anisotropy of short-fiber reinforced composites

Coupled simulation of flow-induced viscous and elastic anisotropy of short-fiber reinforced composites

Studies on the Geometrical Design of Spider Webs for Reinforced Composite Structures

Steering second-order tensor voting by vote clustering

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