*2.3. Three-Point Bending Test Simulation*

The influence of the interface modification on the structural deformation and failure behaviour is investigated by modelling an impact-loaded three-point bending beam setup (Figure 5a). The supports and the load introduction are modelled with rigid shell elements. The indenter moves downwards at a constant velocity of 2 m/s for a total displacement of 20 mm. Each prepreg layer is modelled by two elements in the thickness direction using reduced integrated hexahedral elements (ELFORM 1). The element size is 1 mm in the longitudinal axis and 3.33 mm in the width direction, resulting in 5964 solid elements. In addition, potential delamination layers are distributed symmetrically to the centre plane corresponding to the experimental setup [10] with 1 μm thick cohesive elements (ELFOR 19), resulting in 1065 cohesive elements. A segment-based automatic surface-to-surface contact

with a friction coefficient of 0.3 [19] is used to enable contact between the composite plies after the cohesive elements have failed.

**Table 2.** Cohesive properties.


**Figure 5.** (**a**) Geometry of three-point bending test. (**b**) Force–displacement curve with according energies.

The test is evaluated using the force–displacement curve (Figure 5b). The curve's integral equals the total absorbed energy *ET*. The integral up to the force maximum is referred to as initiation energy *EI* and corresponds largely to the elastic energy stored in the test specimen. The remaining energy is referred to as propagation energy *EP* and is largely related to damage and failure processes in the test specimen.

To improve the energy absorption capacity of impact-loaded CFRP structures, the total energy absorbed *ET* should be maximised. In the case presented here, this can be achieved by maximising the propagation energy without significantly reducing the initiation energy. Furthermore, the structural integrity of such CFRP composites can be improved by the initiation and propagation of delaminations.

## *2.4. Optimisation Strategies*

The desired increase of energy absorption and structural integrity of the impact-loaded CFRP beam is approached using three different interface designs (Figure 6). The interlaminar properties of all five interfaces are uniformly weakened by varying the interlaminar contact area in design A (Figure 6a). Design B establishes whether a layer-by-layer weakening of the interface leads to a further increase in energy absorption (Figure 6b). Finally, sectional interface modifications are used in the third concept to determine which positions are particularly suitable for weakening in design C (Figure 6c).

**Figure 6.** Investigated interface modification designs.

The software LS-Opt is used to carry out the optimisation [20]. A metamodel-based optimisation of the resulting 15 model input parameters is performed using a sequential approach, which reduces the parameter space in each iteration (see Figure 7).

**Figure 7.** Framework of the applied metamodel-based optimisation.

A design of experiment (DoE) is created using Latin hypercube sampling. FE simulations are then generated for each parameter set. Based on these results, a feedforwarded neural network (FFN) metamodel is trained using standard LS-Opt settings. The FFN approximates the relationship between the interface parameters *κ<sup>i</sup>* and the total energy absorption *ET*. The input parameters are then optimised based on the predictions of the metamodel. The ASA (adaptive simulated annealing) algorithm is used for optimisation. The sequential optimisation is terminated when the parameter sets or the objective function differ less than 1% from the previous iteration. If this is not the case, new parameter sets are generated, whereby the parameter set domain is reduced by 20%.
