PSI - Issue 52

408 Pascal Alexander Happ et al. / Procedia Structural Integrity 52 (2024) 401–409 Author name / Structural Integrity Procedia 00 (2019) 000–000 A further study was conducted for different particle-volume-fractions ℎ � = 2, 4, 6, 8, 10 and 12%, where the elastic parameters of the individual layers were adopted from the previous optimization procedure. The surrogates employed 5 layers, as this minimized the computational cost in comparison to a higher number of layers, while still being very accurate, as previous studies have shown that the quality of the predictions the surrogate achieves is not sensitive to the number of layers employed. The numerical evaluation was conducted for surrogates and its corresponding accurate particle of the shape of � � , � � � for the base sphere radii of r = 0.6, 1.6. The obtained results of the Young’s modulus were normalized with the Young’s modulus of the matrix material, see Fig. 7 below. 8

Fig. 7: The normalized modulus for accurate and surrogate model with 5 layers. The results obtained for the different particle-volume-fractions of the surrogate particles are close to the results obtained for accurate particles. A nonlinear relationship between the effective Young’s modulus and the particle volume-fraction can be observed, where the surrogate model can capture this behavior as well. The deviation between the two obtained curves for each particle is small. Further studies need to be carried out to address this issue. 5. Conclusions Particle reinforced composites are as versatile as they are complex to model and to evaluate their elastic properties. The presented study proposes to reduce the computational effort for particles with complex shapes by using surrogate models. These surrogate models can be approximated as layered spheres where the elastic properties of each layer are calculated using any standard homogenization method in combination with an optimization procedure to achieve a good approximation of the surrogate compared to its accurate particle counterpart. In presented studies the first approximation of the elastic properties were obtained using Reuss and Voigt bounds, and further optimized for every layer with the use of the heuristic method of Particle Swarm Optimization. The Reuss and Voigt approximations lead to an over- and under estimation respectively of the obtained Young’s modulus of the studied composite. The effective elastic properties of the surrogate model are in good agreement with the effective elastic properties of the corresponding accurate model (see Fig. 7), considering the different particle volume fractions studied. The results obtained for the surrogate models regarding E deviate only slightly, which can be the result of coarse meshing of the FEM model. Further research has to be conducted in regards to the sensitivity of the surrogate models to the mesh fidelity. The surrogate models can therefore be used to reduce the computational cost without the drawback of