Effective elastic properties of composites with particles of polyhedral shapes

Contributions of 15 convex polyhedral particle shapes to the overall elastic properties of particle-reinforced composites are predicted using micromechanical homogenization and direct finite element analysis approaches. The micromechanical approach is based on the combination of the stiffness contribution tensor (N-tensor) formalism with Mori-Tanaka and Maxwell homogenization schemes. The second approach involves FEA simulations performed on artificial periodic representative volume elements containing randomly oriented particles of the same shape. The results of the two approaches are in good agreement for volume fractions up to 30%. Applicability of the replacement relation interrelating N-tensors of the particles having the same shape but different elastic constants is investigated and a shape parameter correlated with the accuracy of the relation is proposed. It is concluded that combination of the N-tensor components of the 15 shapes presented for three values of matrix Poisson's ratios with the replacement relation allows extending the results of this paper to matrix/particle material combinations not discussed here.