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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The base radius of the sphere was varied, to influence the relation of the undulation’s amplitude to the undisturbed core of the sphere. The process of creation and the resulting particle shapes obtained using Python (2023) are displaced in Fig. 2.

Fig. 2: Particle approximation created with the use of LSH: The different LSH undulations e.g. � � , � � � , � � � are generated onto spheres with radii = 0.6, 1.1, 1.6 . The resulting particle shapes approximate the shape of the studied particles more closely in comparison to approximation through ellipsoids. The finite element method as proposed by Happ and Piat (2022), can be used to evaluate the influence of complex particle shapes (e.g. depicted in Fig. 2) on the elastic properties of the corresponding particle reinforced composite, but this comes at the expense of being computationally costly, even if the numerical study is limited to only a few particles. In the following studies the results of the calculations which use particle approximations obtained with the LSH method with a fine FE mesh, calculated as presented by Happ and Piat (2022), will be utilized for the verification of the proposed approximations and will be referred in the following as accurate particle. The computational cost becomes prohibitive for a numerical study, if many particles are used to create a real microstructure. To solve this problem, the new method which includes the so-called surrogate creation method is proposed in these studies. 2.2 Surrogate creation Surrogates of the particles approximation, have been developed to reduce the computational complexity of the simulations. The surrogates take into account the undulations of the particle shape and superpose it to a surface containing no undulations. The surrogate particles are created by slicing the accurate particle into a core sphere, which stretches from the center of the particle to the lower end of the undulations. The undulated section of the particle is then cut into layers, where the volume of the particle and the matrix in layers are evaluated and then used to calculate the effective elastic properties of that specific layer.