PSI - Issue 52

Pascal Alexander Happ et al. / Procedia Structural Integrity 52 (2024) 401–409 Author name / Structural Integrity Procedia 00 (2019) 000–000

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increase in the radius of the sphere. This might be due to the effect of the undulation on the material distribution of the particle. An increase in the amplitude in comparison to the base sphere leads to more material being distributed outside of the core sphere, which stretches from the center of the particle to the bottom of the amplitude. With small base spheres more material is distributed throughout volume between undulated surface and inner, undisturbed sphere in contrast to big base spheres, where comparatively less material is distributed outside of the core sphere. A more pronounced deviation between the predictions for the Young’s modulus in comparison between the different radii of the base spheres can be seen in Fig. 5 (right) in for the particle with the surface shape � � � .

Fig. 5: The normalized modulus of the surrogate models for particles with undulations shapes � � (left) and � � � (right) (for different ) as a function of number of layers obtained using Reuss, Voigt and PSO methods. The PSO method to obtain the effective elastic properties of the individual layers is not sensitive to the number of used layers for the surrogate model. The studies show that good predictions of the modulus of the composite can be achieved. The above-described procedure was repeated for a layer count of 5 for the particle surface shapes � � , � � � for the radii of the base sphere of = 0.6,0.8,1.0,1.2,1.4,1.6 . The results of this study are displayed in Fig. 5 above and a good agreement between the obtained results for the accurate models and their corresponding surrogates was obtained. The surrogate modeling method was able to approximate the material properties of the accurate particles.

Fig. 6: The normalized modulus was obtained for surrogates consisting of 5 layers, for a particle-volume-fraction ℎ 2 = 7% .