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

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.