Geometric structure model of plain woven fabric based on progressive spring-slide mechanics

The geometric structure of woven fabric affects the appearance and physical properties and can be used to predict the weavability of the fabric. An accurate description of the structure is beneficial to predict the characteristics and the appearance of the woven fabric. The purpose of the study is to build an accurate, realistic, and stable three-dimensional (3D) geometric structure model based on the mechanics for plain woven fabrics. Parameters such as the initial Young's modulus of the yarn materials, thicknesses, warp density, pre-loaded tension on the yarns, and the amount of letting-off and taking-up are considered in the model. The yarns are simplified as a series of spring-sliders that are stretched in the fabric and moved along the direction of the resultant forces step by step according to the changing forces. The yarns stop moving when all the forces reach equilibrium. The tests demonstrate that the algorithm conforms to the weaving principles. The 3D images of the geometric structure of the woven fabric at different steps are displayed by B-spline surface modeling technology. A Keyence VH600 micro-measurement system is used to measure the 3D coordinates of the real fabric accurately without destroying the fabric structure. The similarity of the real geometric structure and the calculated geometric model is evaluated by calculating the discrete Fréchet distances. The result validates that the similarity of the calculated geometric structure and the measured value is more than 90% for both the warp and weft direction.