A New Orientation Density Function of Ideally Migrating Fibers to Predict Yarn Mechanical Behavior

A novel control of a texture goniometer, which depends on the texture being measured itself, is suggested. In particular, it is suggested that the obsolete control with constant step sizes in both angles is replaced by an adaptive successive refinement of an initial coarse uniform grid to a locally refined grid, where the progressive refinement corresponds to the pattern of preferred crystallographic orientation. The prerequisites of this automated adaptive control is the fast inversion of pole intensities to orientation probabilities in the course of the measurements, and a mathematical method of inversion that does not require a raster of constant step sizes and applies to sharp textures.

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The de la Vallée Poussin Standard Orientation Density Function

Textures and Microstructures ◽

10.1155/tsm.33.365 ◽

1999 ◽

Vol 33 (1-4) ◽

pp. 365-373 ◽

Cited By ~ 15

Author(s):

H. Schaeben

Keyword(s):

Density Function ◽

Series Expansion ◽

Harmonic Series ◽

Exact Representation ◽

Standard Orientation ◽

Orientation Density ◽

De La Vallée Poussin

The de la Vallée Poussin standard orientation density function νκ(ω)=C(κ)cos⁡2κ(ω/2) is discussed with emphasis on the finiteness of its harmonic series expansion which, advantageously distinguishes it from other known standard functions. Given its halfwidth, the de la Vallée Poussin standard orientation density function allows, for example, to tabulate the degree of series expansion into harmonics required for its exact representation.

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ON THE DEVELOPMENT OF COMPRESSIBLE PSEUDO-STRAIN ENERGY DENSITY FUNCTION FOR HYPERELASTIC MATERIAL: EXPERIMENT, THEORY AND FEM

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-2005-0028 ◽

2005 ◽

Vol 29 (3) ◽

pp. 459-475

Author(s):

Hamid Ghaemi ◽

A. Spence ◽

K. Behdinan

Keyword(s):

Mechanical Behavior ◽

Density Function ◽

Energy Function ◽

Strain Energy ◽

Three Dimensional ◽

Strain Energy Function ◽

Material Parameter Identification ◽

Constitutive Function ◽

Strain Energy Density Function ◽

Biaxial Tests

This study was carried out to develop a compressible pseudo-strain energy function that describes the mechanical behavior of rubber-like materials. The motivation for this work was two fold; first was to define a single-term strain energy function derived from constitutive equations that can describe the mechanical behavior of rubber-like materials and taking into account the coupling between principal stretches and the nearly incompressibility characteristic of elastomers. Second was to implement this strain energy function into the Finite Element Method (FEM) to study the suitability of the model in FEM. A one-term three-dimensional strain energy function based on the principal stretch ratios was proposed. The three dimensional constitutive function was then reduced to describe the behavior of rubber-like materials under biaxial and uniaxial loading condition based on the membrane theory. The work presented here was based on the decoupling of the strain density function into a deviatoric and a volumetric part. Using pure gum, GMS-SS-A40, uniaxial and equi-biaxial experiments were conducted employing different strain rate protocols. The material was assumed to be isotropic and homogenous. The experimental data from uniaxial and biaxial tests were used simultaneously to determine the material parameters of the proposed strain energy function. A GA curve fitting technique was utilized in the material parameter identification. The proposed strain energy function was compared to a few well-known strain energy functions as well as the experimental results. It was determined that the proposed strain energy function predicted the mechanical behavior of rubber-like material with greater accuracy as compared to other models both analytical and numerical results.

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Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution

NeuroImage ◽

10.1016/j.neuroimage.2004.07.037 ◽

2004 ◽

Vol 23 (3) ◽

pp. 1176-1185 ◽

Cited By ~ 987

Author(s):

J.-Donald Tournier ◽

Fernando Calamante ◽

David G. Gadian ◽

Alan Connelly

Keyword(s):

Density Function ◽

Fiber Orientation ◽

Diffusion Weighted Mri ◽

Direct Estimation ◽

Spherical Deconvolution ◽

Diffusion Weighted ◽

Orientation Density

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Orientation Analysis

Materials Science Forum ◽

10.4028/www.scientific.net/msf.1016.605 ◽

2021 ◽

Vol 1016 ◽

pp. 605-610

Author(s):

Janos Imhof

Keyword(s):

Density Function ◽

Initial Function ◽

Minimum Principle ◽

Density Functions ◽

Pole Density ◽

Orientation Analysis ◽

Euler Space ◽

Orientation Density ◽

Basic Concepts ◽

The Relationship

Simple figures illustrate the basic concepts: orientation, Euler angles, Euler space, orientation density function, pole density function. The iteration that decisively influenced the development of orientation analysis follows directly from the relationship between the two density functions. The minimum principle defines the initial function and the structure of the iteration. Using model orientation density function, we prove that this kind of orientation analysis is extremely effective.

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