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.