Artificial neural network-assisted theoretical model to predict the viscoelastic–plastic tensile behavior of polyamide-6 multi-ply yarns

Multi-ply yarns have been used as the main structure to form strands, braids, and fabrics. Thus, various strategies including experimental, numerical, and analytical models have been utilized to predict their tensile behavior. In analytical models, all are limited to a specific number of fibers in an elastic region. The time-consuming experimental-based studies suffer from the accuracy of subjective results, associated errors of the experiment, ignoring the physical aspect of the problem, and practical issues during the controlling of variables. Concerning the numerical approaches, no insight into generalization is provided and they are bug-prone methods. In this study, a generalized method is developed to predict the whole tensile behavior of polyamide-6 (PA-6) multi-ply yarns with an open-packing structure. This approach is a combination of two geometrical models and an artificial neural network that enable the calculation of the deformation of fibers in different layers, the number of fibers in each layer by taking the gap into account, and an artificial neural network to map from parameters including strain and rate of strain to the reacting force on monofilament. The model has been verified by numerical analysis and examination of several factors including the number of layers, twist level, and rate of strain. After having trained ANN modeling with R2≈1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}^{2}\approx 1$$\end{document}, the proof-of-concept results demonstrated that this established model is capable of predicting the tensile behavior of PA-6 multi-ply yarns with high precision and accuracy (average value of R2=0.97\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}^{2}=0.97$$\end{document} and MAPE=4.65%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{MAPE}=4.65 \%$$\end{document}). It is envisioned that the presented model can be extensively applied to all yarns.