Validation of a New Closure Model for Flow-Induced Alignment of Fibers

2000 ◽  
Author(s):  
A. Imhoff ◽  
S. Parks ◽  
C. Petty ◽  
A. Bénard
Keyword(s):  
Distribution Function ◽  
Fiber Orientation ◽  
Numerical Solutions ◽  
Exact Distribution ◽  
Short Fibers ◽  
Closure Model ◽  
Order Tensor ◽  
Orientation State ◽  
Exact Distribution Function ◽  
Fourth Order Tensor

Abstract A closure model for flow-induced orientation of short fibers is presented and discussed. The model retains all the six-fold symmetry and contraction properties of the fourth order tensor. A derivation of the model is presented and the conditions required for the model to be realizable are discussed. The model is validated against analytical and numerical solutions of the exact distribution function for the fiber orientation state for different flow fields. Variations of this model and its limitations are also discussed.

On inelasticity of damaged quasi rate independent anisotropic materials

2018 ◽  
Vol 24 (3) ◽  
pp. 778-795 ◽  
Author(s):  
Milan Mićunović ◽  
Ljudmila Kudrjavceva
Keyword(s):  
Effective Field ◽  
Short Fibers ◽  
Viscoplastic Strain ◽  
Order Tensor ◽  
Two Phase ◽  
Elastic Symmetry ◽  
Field Approach ◽  
Steel Aisi ◽  
Stainless Steel Aisi ◽  
Fourth Order Tensor

This paper deals with a body that has a random 3D-distribution of two phase inclusions: spheroidal mutually parallel voids, and differently oriented reinforcing parallel stiff spheroidal short fibers. By the effective field approach the effective stiffness fourth order tensor is formulated and found numerically. Simultaneous and sequential embeddings of inclusions are compared. Damage evolution is described by a modified Vakulenko approach to the endochronic thermodynamics. A brief account of the problem of effective elastic symmetry is considered. The results of the theory are applied to the damage-elasto-viscoplastic strain of a reactor stainless steel AISI 316H.

Orientation Distribution of Fiber Suspensions in Extensional Flow

2013 ◽  
Vol 785-786 ◽  
pp. 981-984 ◽  
Author(s):  
Zan Huang ◽  
Jin Ping Qu ◽  
Ji Wei Geng ◽  
Shu Feng Zhai ◽  
Shi Kui Jia
Keyword(s):  
Differential Equation ◽  
Distribution Function ◽  
Orientation Distribution Function ◽  
Fiber Orientation ◽  
Extensional Flow ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Fiber Suspensions ◽  
Short Fibers ◽  
Fiber Orientation Distribution

An orientation distribution function is adopted to describe three-dimensional orientation distribution of short fibers suspensions in extensional flow. A mathematical model of evolution process on fiber orientation distribution function is established by analytical method. Numerical simulation is also used to describe two and three dimensional orientation distribution of fibers. Therefore, analytical solution of differential equation on forecast fiber orientation distribution is deduced.

EVALUATING MEAN INTRINSIC CURVATURE OF DISORDERED SEMIFLEXIBLE BIOPOLYMERS

2012 ◽  
Vol 26 (24) ◽  
pp. 1250131 ◽  
Author(s):  
CHIN-YI HUNG ◽  
ZICONG ZHOU ◽  
YUAN-SHIN YOUNG ◽  
FANG-TING LIN
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Power Law ◽  
Short Range ◽  
Exact Distribution ◽  
Two Dimensional ◽  
Intrinsic Curvature ◽  
Short Range Correlation ◽  
Range Correlation ◽  
Exact Distribution Function

We study two-dimensional disordered semiflexible biopolymers with finite mean intrinsic curvature (MIC). We find exact distribution function of orientational angle for the system with short-range correlation (SRC) in intrinsic curvatures. We show that with a finite MIC, our theoretical end-to-end distances can be fitted well to some experimental data of DNA with long-range correlation (LRC) in sequences. Moreover, we find that the variance of the orientational angle has the same power-law behavior as that of the bending profile for DNA with LRC in sequences. Our results provide a way to evaluate MIC and suggest that the LRC in sequences can result in a SRC in intrinsic curvatures.

Dynamics Analysis of Orientation Distribution of Fiber Suspensions in Shear-Extensional Flow

2014 ◽  
Vol 709 ◽  
pp. 168-171
Author(s):  
Pei Fang Luo
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Distribution Function ◽  
Fiber Orientation ◽  
Extensional Flow ◽  
Orientation Distribution ◽  
Dynamics Analysis ◽  
Fiber Suspensions ◽  
Short Fibers ◽  
Uniaxial Extensional Flow

A mathematical model on orientation distribution function of short fibers suspensions in shear-uniaxial extensional flow is established. Furthermore, the result of differential equation on fiber orientation can be obtained.

A Statistical Method to Obtain Material Properties From the Orientation Distribution Function for Short-Fiber Polymer Composites

Materials ◽  
2005 ◽  
Author(s):  
David A. Jack ◽  
Douglas E. Smith
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Material Properties ◽  
Fiber Orientation ◽  
Orientation Distribution ◽  
Short Fiber ◽  
Expectation Values ◽  
Order Tensor ◽  
Fiber Orientation Distribution ◽  
Orientation Tensors

Material behavior of short-fiber composites can be found from the fiber orientation distribution function, with the only widely accepted procedure derived from the application of orientation/moment tensors. The use of orientation tensors requires a closure, whereby the higher order tensor is approximated as a function of the lower order tensor thereby introducing additional computational errors. We present material property expectation values computed directly from the fiber orientation distribution function, thereby alleviating the closure problem inherent to orientation tensors. Material properties are computed from statistically independent unidirectional fiber samples taken from the fiber orientation distribution function. The statistical nature of the distribution function is evaluated with Monte-Carlo simulations to obtain approximate stiffness tensors from the underlying unidirectional composite properties. Examples are presented for simple analytical distributions to demonstrate the effectiveness of expectation values and results are compared to properties obtained through orientation tensors. Results yield a value less than 1.5% for the coefficient of variation and suggest that the orientation tensor method for computing material properties is applicable only for the case of non-interacting fibers.

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