Geometrical analysis of auxetic woven fabrics based on foldable geometry

This paper reports a geometrical analysis of auxetic woven fabrics based on foldable geometry. Two fabrics having different geometrical parameters were first designed and fabricated and then subjected to tensile tests in two principal directions. Based on the experimental observations of the geometry of one fabric structural unit cell at different tensile strains, a geometrical model was first proposed and a relationship between the Poisson's ratio and tensile strain was then established for each principal direction. Two semi-empirical equations are subsequently obtained for both principal directions by fitting the established relationships with experimental results. After validation by the experimental results of the other fabric, the obtained semi-empirical equations were finally used to predict the auxetic behavior of the fabric with a given geometrical parameter. The calculated and experimental results are found to be in excellent agreement with each other. Therefore, the semi-empirical equations obtained in this study could be useful in the design and prediction of the auxetic behavior of auxetic woven fabrics made with the same type of materials and foldable geometry but with different values of geometrical parameters.