Carbon fabric 3D modeling according to nonlinear bending theory

In this paper we present approaches to creating a 3D solid model of a fabric based on a preliminary calculation of its structure parameters based on a nonlinear bending theory. The mathematical model is proposed for forecasting the structure parameters of the grey fabric made of carbon yarns. Technique of building up the fabric three-dimensional model, consisting of many surfaces simulating warp and weft yarns, derived based on surface equations that specify the yarns contours, is presented following the fabric structure parameters calculations. The advantage of this approach is the ability to accurately simulate the place of contact of the yarns in the fabric and eliminates interpenetration between yarns in fabric. It is possible to use an explicit definition of the surface equation that limits the volume of the thread in the fabric. This allows significantly simplifying the model and conducting direct calculations of the coordinates of surface points (yarn surface). Surface equations for the yarn description in a fabric taking into consideration the lateral bending, dimensions variations of yarn cross-section and its shape along centre line are offered.