Correlation between surface-to-volume ratio of the particle shape and elastic properties of the particulate composites

Abstract

This work is motivated by real-world particle shapes, observed using a scanning electron microscopy. The focus of the presented studies was to understand the influence of the particle shapes on the effective elastic properties of the two-phase composites. For this, particles with polyhedral, undulated and other shapes were numerically modeled using analytical functions. Creation of some shapes, like polyhedral, are known from the literature but Laplace’s spherical harmonics, as well as the Goursat’s surface and some others, were used for the first time to create novel particle shapes. Elastic properties of the composites with different particle shapes were calculated using the finite element analysis. The obtained results show good agreement with mean-field homogenization methods such like Mori-Tanaka and Lielens as well as other numerical results available in the literature. Further, the dependence of the effective Young’s moduli of the composite on the shape and the corresponding surface-to-volume ratio of the particles was studied. It was observed that the effective Young’s moduli increase with the surface-to-volume ratio of the particles in the case where particles are stiffer in comparison to the matrix. It was also remarked that, in the case of particles of similar shapes, the particle surface-to-volume ratio and the effective Young’s moduli differ significantly with the surface curvature and the edge sharpness of the particles.