Prediction of textile geometry using an energy minimization approach

In this article, a numerical method to predict textile geometry is derived using a technique based on finite elements (FEs). A geometric modeling package is used to represent an initial geometry of the yarns within the textile. The yarn mid-surface is then represented using plate elements, with the yarn thickness and cross-section being reconstructed from this mid-surface. The bending and tensile aspects of the yarn behavior are represented by separate features of the plate elements and the total energy for the system is minimized. Contacts are modeled using a penalty method, where the contact force is proportional to penetration distance. Once geometry correction has been achieved by solving the FE problem, the geometric model of the textile is corrected to take into account the predicted movements of the yarns. For validation purposes, the method is applied to two-dimensional (2D) and three-dimensional (3D) weaves and compared against images of the real fabrics. Agreement between predictions and images is good for the 3D weave and excellent for the 2D weave.