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.

中文翻译：

---

替代模型在 3D 旋转对称颗粒复合材料有效弹性性能数值评估中的应用


具有非椭圆形颗粒形状的颗粒复合材料的微机械建模提出了重大挑战，因为无法使用基于 Eshelby 基本结果的分析方法。另一方面，当颗粒特征具有小曲率半径、尖锐边缘并且需要极细网格时，通过有限元分析进行直接数值评估可能会涉及较高的计算成本。本文建议用替代模型代替精确的颗粒形状，对有效弹性模量产生大致相同的贡献。我们通过考虑旋转对称 3D 粒子形状（其外表面由拉普拉斯球谐函数定义）来说明我们的方法。在这种情况下，球形分层代理提供了良好的近似精度，特别是当每层的材料参数由粒子群优化算法确定时。通过考虑几种高度波动的颗粒形状并将替代模型结果与原始微观结构的直接有限元模拟进行比较，提出了所提出的方法。