Effects of the inclusion shape, arrangement, and volume fraction on effective elastic moduli of two-dimensional two-phase composites

The spatial arrangement and shape of inclusions can have a major impact on two-phase composites' mechanical properties. Few studies consider the coupling effects of these two factors on the effective elastic moduli of two-phase composites. This study introduces the circularity of inclusions to modify the three-point approximation (TPA) for quantitatively predicting the coupling effects of inclusion planar arrangement and shape. Two-dimensional particle packing structures of monosized particles are generated with polygons, superellipses, and superovals of different circularities and volume fractions via the ordered arrangement approach or the discrete element method. Then, the lattice model is conducted on the particle packing structures to verify the reliability of the modified TPA. The comparison between the theoretical calculation and the numerical simulation indicates that our modified TPA can predict the effects of planar arrangement, shape, and volume fraction of inclusions on the effective moduli. The proposed modified TPA offers fresh perspectives on comprehending intricate relationships between the macro-property and composition of composites.