Assessing the use of Tensor Closure Methods with Orientation Distribution Reconstruction Functions
Assessing the use of Tensor Closure Methods with Orientation Distribution Reconstruction Functions
复制标题
评估张量闭合方法与方向分布重建函数的使用
DOI：
10.1177/0021998304048413
复制
发表时间：
2004
影响因子：
2.9
通讯作者：
Douglas E. Smith
中科院分区：
文献类型：
--
作者：
D. Jack;Douglas E. Smith
在短纤维增强复合材料系统的充型模拟中，取向张量被广泛地用来描述纤维取向。在这些流动计算中，采用了一个闭包，将四阶取向张量近似为二阶取向张量的函数。还提出了六级关闭的建议。本文通过用傅里叶级数表示的连续高阶取向张量重建纤维取向分布函数，评估了闭合近似在纤维取向预测中的效果。这种方法认识到取向张量与分布函数的级数展开系数有关。引入并应用了一种误差度量，它使得比较不同阶的闭包成为可能。研究了与几个四阶闭合和六阶闭合有关的误差，并与由准确的二阶、四阶和六阶取向张量重建所产生的截断误差进行了比较。给出了注塑纤维增强复合材料的一系列相互作用系数和典型流场的算例，以说明所提出的闭合评估方法。
Orientation tensors are widely used to describe fiber orientations in mold filling simulations of short-fiber-reinforced composite systems. In these flow calculations, a closure is employed that approximates the fourth-order orientation tensor as a function of the second-order orientation tensor. Sixth-order closures have also been proposed. This paper assesses the effect of using closure approximations in fiber orientation predictions by reconstructing the fiber orientation distribution function from successively higher order orientation tensors in a Fourier series representation. This approach recognizes that the orientation tensors are related to the series expansion coefficients of the distribution function. An error metric is introduced and applied that makes it possible to compare closures of varying order. Errors associated with several fourth-order closures and a sixth-order closure are investigated and compared with the truncation error that results from a reconstruction of the exact second-, fourth-, and sixth-order orientation tensors. Examples are provided over a range of interaction coefficients and flow fields typical of injection molded fiber-reinforced composites to illustrate the proposed closure assessment method.