Geometrical Anisotropy in Biphase Particle Reinforced Composites

Particle shape plays a crucial role in the design of novel reinforced composites. We introduce the notion of a geometrical anisotropy index $A$ to characterize the particle shape and establish its relationship with the effective elastic constants of biphase composite materials. Our analysis identifies three distinct regions of $A$⁠: (i) By using ovoidal particles with small $A$⁠, the effective stiffness scales linearly with $A$ for a given volume fraction $α$⁠; (ii) for intermediate values of $A$⁠, the use of prolate particles yield better elastic properties; and (iii) for large $A$⁠, the use of oblate particles result in higher effective stiffness. Interestingly, the transition from (ii) to (iii) occurs at a critical anisotropy $Acr$ and is independent of $α$⁠.