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A variable metric stochastic theory of textile composites with random geometric parameters of yarn cross-section

机译：纱线横截面几何参数随机的织物复合材料的可变度量随机理论

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A variable metric stochastic theory of the elastic constants of textile composites with stochastic yarn (or tow) geometry has been developed in the current study. A variable metric coordinate transformation is utilized in this theory to introduce the cross-section shape fluctuations of yarn into the compliance of textile composites. Six parameters are defined to describe the positioning and cross-section shape of yarn completely. Then, the Taylor expansions of the local stochastic variable metric basis and the compliance of yarn are executed. Finally, the volumetric averaging method is employed to obtain the elastic properties of textile composites. The numerical simulations show that the fluctuations of geometric parameters may affect the elastic response of textile composites considered. The example of single straight yarn proves the validity of the theory and presents the explicit formulas of influence of stochastic yarn geometry on elastic constants. Within the example of plain weave composite, random yarn cross-section shape and twist degrade all of the elastic constants except the shear moduli and Poisson's ratios in 1-3 and 2-3 directions, which are determined by the comprehensive effect of the stochastic scaling and twist. (C) 2015 Elsevier Ltd. All rights reserved.
机译：在当前研究中，已经开发出具有随机纱线（或丝束）几何形状的纺织品复合材料的弹性常数的可变度量随机理论。在该理论中，采用了可变的公制坐标变换，将纱线的横截面形状波动引入到纺织品复合材料的柔度中。定义了六个参数来完整描述纱线的位置和横截面形状。然后，执行局部随机变量度量基础的泰勒展开和纱线的柔度。最后，采用体积平均法获得织物复合材料的弹性。数值模拟表明，几何参数的波动可能会影响所考虑的纺织品复合材料的弹性响应。单根直纱的例子证明了该理论的有效性，并提出了随机纱线几何形状对弹性常数的影响的明确公式。在平纹复合材料的示例中，随机纱线的横截面形状和捻度会降低所有弹性常数，但在1-3和2-3方向上的剪切模量和泊松比除外，这由随机定标的综合效应决定和扭曲。 （C）2015 Elsevier Ltd.保留所有权利。

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