### 5.1.2. Draping Procedure

The draping simulation in ACP uses an energy algorithm. In this approach, a reinforced ply is idealized with a pin joint net model ([ 1 ] and [ 6 ]). The net consists of unit cells, which are constructed of inextensible bi-directional fibers that are pinned together at crossover node points. The deformation of the fabric takes place by pure rotation of the fibers around the pins as illustrated in Figure : Deformation of the Draping Unit Cell.

Figure : Deformation of the Draping Unit Cell

In draping simulation, draping unit cells are laid one by one on the surface of the model so that they are fully in contact with the surface. The draping procedure involves the search for two types of draping cells: those with two or three known node points as shown in Figure : Draping Scheme. In case of three known node points, the search algorithm seeks the fourth node point from the surface so that the distances along the surface to the adjacent node points are equal to a unit cell side length.

Figure : Draping Scheme

The above figure shows draping of a cell that has two or three known node points (left/middle) and propagation scheme using orthogonal directions (right).

When two node points are known and the locations of the other two must be determined, the search algorithm is based on the minimization of the shear strain energy [ 4 ]:

| (5–1)

where G is the elastic shear modulus of the uncured reinforcement. The shear deformation is related to the angle α between the originally orthogonal fibers [ 3 ]:

| (5–2)

The total shear strain energy of the draping cell is defined as the sum of energy computed at the four corners. The two constants can be excluded and the minimization problem becomes:

| (5–3)

From this, the locations of the two node points can be determined with an iterative minimization algorithm.

The draping simulation starts from a given seed point and progresses in the given draping direction. In this phase each draping cell initially has two known node points. Draping cells are laid until the model edge is reached. Then, the procedure is repeated in the opposite direction (if applicable) and in the orthogonal directions (Figure : Draping Scheme). After the main draping paths have been determined, the cells with three known nodes are populated. The algorithm resolves if the whole model is draped or if there are areas where the draping simulation needs to be restarted.

The simulation determines fiber principal directions. These directions are mapped to the finite element model to correct laminate lay-ups accordingly. The shearing angle β is defined as

| (5–4)

It expresses the deviation from the ideal non-sheared case. The visualization of β values over the model surface is useful for depicting problem areas. For most fabric reinforcements, the maximum deformation angle α is 30-40 degrees [ 7 ]. When a fabric is sheared to a specific deformation level, the shear force starts to increase radically with only little increase in the shear deformation. This limit is called the locking angle, and beyond it buckling is observed. The locking angle of a reinforcement can be determined experimentally [ 5 ].

The pin joint net model is specifically developed for woven fabrics, but it has been proven to work for cross ply prepreg stacks and also for single unidirectional plies when the deformation is moderate [ 8 ].

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