Project FibraGen

In this project, a hybrid finite element-geometric algorithm for draping simulation of fiber-reinforced composites over a triangulated 3D surface is presented. Unlike other kinematic approaches, which are purely geometrical and do not consider material properties at all, in the presented method, some structural properties representing actual mechanical properties of composite materials are taken into account without affecting the speed of the algorithm.

This draping technique is built upon the fact that the fabric draping is optimum when the amount of distortions (wrinkles) in it is minimal. In this algorithm, a fabric, before draping, is considered as a group of square (or rectangular) cells, and each cell is modeled by four side springs and two diagonal springs (Figure 1). These assumptions cause a trade-off between the accuracy and speed of draping simulation. However, the generated results could be trustworthy for the majority of cases, and if more accurate modeling is required, other techniques exploiting pure finite element analysis (FEA) could be implemented with considerably higher computational costs. Figure 2 shows the difference between a pure finite element and a simplified one (our method).

In the draping process, depending on the surface geometry, the fabric can wrinkle and cells may distort and no longer be a perfect square (or rectangular). Shear angle $\alpha$  is used as a representation of wrinkles in the fabric at that location. In other words, the higher the shear angle, the more severe the wrinkles at that location.

Unlike FEA-based methods that require an initial flat (2D) fabric as an input, the algorithm used in this paper does not initiate the simulation from a 2D pattern. This is another advantage of this method over these techniques. The process begins at a given starting point (seed point) and propagation direction (local fiber orientation at the seed point). Other required inputs are:

• The triangulated surface to be covered by the composite material. 

• Surface boundary, i.e., the boundary of the surface to be covered by the composite material. 

• Fabric cell size along the sides. 

• The ratio of spring constants along the sides and diagonal directions. The higher this value, the more resistant the fabric is against stretching along the sides versus that along diagonals, which results in shear

The developed algorithm has now been implemented in Autodesk® TruComposites software. Below are some examples of draping simulations over different 3D molds using the developed method. In all of these, the triangulated surface is the mold and the simulated fiber composite is shown by square meshes. The color shade represents the wrinkle intensity, with dark blue being the minimum wrinkle and dark red the maximum.

Below is a list of my publications on this topic:

• Han, S., Ebrahimi, M. and Morruzi, M., 2017, Three-Dimensional Numerical Flow Simulation of Resin Transfer Molding Process With Draping Analysis, ANTEC.

• Ebrahimi, M., Moruzzi, M. and Iorio, F., Autodesk Inc, 2021. Hybrid structural-geometric technique for performing draping simulation of woven fabric composites. U.S. Patent 11,069,116.