A sequential inverse approach for draping simulations of woven fabrics with anisotropic hyperelastic behavior laws

Simulations of the draping of woven fabrics for the manufacturing of composite parts with complex geometries rely on either the geometrical method, which does not consider the shearing stresses and the external forces, or incremental finite element analyses, which require substantial CPU times. In this study, the one-step finite element method, also referred as the inverse approach in the literature, commonly used for sheet metal forming, is adapted to the woven fabric draping. The main issue of one-step simulations is the convergence of the Newton–Raphson scheme, which relies on an appropriate initial solution estimation. This problem is addressed by a sequential initial solution estimation, based on successive sub-problems with increasing difficulty up to the actual one. Applications of the proposed method on elementary test cases show fast and robust convergence, with CPU times comparable to those of the geometrical method. The proposed method is able to predict the influence of external forces and material hyperelastic mechanical behavior laws on the strain components of interest of woven fabrics, such as the shearing angles between yarns and the yarn elongations.