Why the reciprocal theorem of Poisson's ratios does not hold for some orthotropic flexible textile composites

The reciprocal theorem of the Poisson's ratios presents the main feature of the linear elastic orthotropic materials. However, in this paper, it is shown that it does not hold for some orthotropic flexible textile composites. The coated multi-axial warp knitted fabric (CMWKF) is used to evaluate this phenomenon. The tensile tests, combined with digital image correlation (DIC) technology, are employed to measure the Young's moduli and Poisson's ratios of the CMWKF in the warp (0°) and weft (90°) directions. The findings show that the classical reciprocal theorem does not apply for the CMWKF. To further explain this phenomenon, a theoretical approach is proposed to estimate the Young's moduli and Poisson's ratios of the CMWKF in 0° and 90° directions, respectively. The theoretical predictions highlight that the Poisson's ratios of the CMWKF in 0° and 90° directions are nearly equal, while the Young's moduli in the two directions are different. The theoretical results match well the experimental observations and explain reasonably that the reciprocal theorem is unsuitable for the CMWKF. It is found that the dissatisfaction of the reciprocal theorem results from the instability of the flexible yarns.