Sparse deconvolution of higher order tensor for fiber orientation distribution estimation

2015 ◽  
Vol 65 (3) ◽  
pp. 229-238 ◽  
Author(s):  
Yuanjing Feng ◽  
Ye Wu ◽  
Yogesh Rathi ◽  
Carl-Fredrik Westin
Keyword(s):  
Fiber Orientation ◽  
Orientation Distribution ◽  
Higher Order ◽  
Order Tensor ◽  
Distribution Estimation ◽  
Fiber Orientation Distribution

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.

Effect of Fiber Orientation on the Tensile Strength in Fiber-Reinforced Polymeric Composite Materials

2005 ◽  
Vol 297-300 ◽  
pp. 2897-2902 ◽  
Author(s):  
Jin Woo Kim ◽  
Jung Ju Lee ◽  
Dong Gi Lee
Keyword(s):  
Tensile Strength ◽  
Composite Material ◽  
Fiber Orientation ◽  
Polymeric Composite ◽  
Orientation Distribution ◽  
Fiber Content ◽  
Fiber Reinforced ◽  
Composite Sheet ◽  
Content Ratio ◽  
Fiber Orientation Distribution

The study for strength calculation of one way fiber-reinforced composites and the study measuring precisely fiber orientation distribution were presented. However, because the DB that can predict mechanical properties of composite material and fiber orientation distribution by the fiber content ratio was not constructed, we need the systematic study for that. Therefore, in this study, we investigated what effect the fiber content ratio and fiber orientation distribution have on the strength of composite sheet after making fiber reinforced polymeric composite sheet by changing fiber orientation distribution with the fiber content ratio. The result of this study will become a guide to design data of the most suitable parts design or fiber reinforced polymeric composite sheet that uses the fiber reinforced polymeric composite sheet in industry spot, because it was conducted in terms of developing products. We studied the effect the fiber orientation distribution has on tensile strength of fiber reinforced polymeric composite material and achieved this results below. We can say that the increasing range of the value of fiber reinforced polymeric composite’s tensile strength in the direction of fiber orientation is getting wider as the fiber content ratio increases. It shows that the value of fiber reinforced polymeric composite’s tensile strength in the direction of fiber orientation 90° is similar with the value of polypropylene’s intensity when fiber orientation function is J= 0.7, regardless of the fiber content ratio. Tensile strength of fiber reinforced polymeric composite is affected by the fiber orientation distribution more than by the fiber content ratio.

Assessing the Use of Tensor Closure Methods With Orientation Distribution Reconstruction Functions

Materials ◽  
2003 ◽  
Author(s):  
David A. Jack ◽  
Douglas E. Smith
Keyword(s):  
Distribution Function ◽  
Fourth Order ◽  
Lower Order ◽  
Series Representation ◽  
Orientation Distribution ◽  
Higher Order ◽  
Interaction Coefficients ◽  
Order Tensor ◽  
Orientation Tensor ◽  
Orientation Tensors

Orientation tensors are widely used to describe fiber distri-butions in short fiber reinforced composite systems. Although these tensors capture the stochastic nature of concentrated fiber suspensions in a compact form, the evolution equation for each lower order tensor is a function of the next higher order tensor. Flow calculations typically employ a closure that approximates the fourth-order orientation tensor as a function of the second order orientation tensor. Recent work has been done with eigen-value based and invariant based closure approximations of the fourth-order tensor. The effect of using lower order tensors tensors in process simulations by reconstructing the distribution function from successively higher order orientation tensors in a Fourier series representation is considered. This analysis uses the property that orientation tensors are related to the series expansion coefficients of the distribution function. Errors for several closures are investigated and compared with errors developed when using a reconstruction from the exact 2nd, 4th, and 6th order orientation tensors over a range of interaction coefficients from 10−4 to 10−1 for several flow fields.

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