On application of a surrogate model to numerical evaluation of effective elastic properties of composites with 3D rotationally symmetric particles

Micromechanical modelling of particulate composites with non-ellipsoidal particle shapes presents significant challenges because analytical approaches based on the fundamental results of Eshelby cannot be used. On the other side, direct numerical evaluations by finite element analysis can involve high computational cost in the case when particle features have small radius of curvature, sharp edges and require extremely fine meshes. This paper proposes substituting the exact particle shape with a surrogate model producing approximately the same contribution to the effective elastic moduli. We illustrate our approach by considering rotationally symmetric 3D particle shapes with the external surface defined by the Laplace's spherical harmonics. In this case, spherical layered surrogates offer good accuracy of approximation, especially when the material parameters of each layer are determined by the particle swarm optimization algorithm. The proposed approach is presented by considering several highly undulated particle shapes and comparing the surrogate model results with direct finite element simulations of the original microstructure.