Elastic modelling of periodic composites with particle interactions

The mechanical properties of periodic composites containing identical spherical particles are investigated using the principles of micromechanics and homogenization procedures. The averaged strain and stress fields are derived in terms of an eight-particle interaction. The effective elasticity with the cubic symmetry tensor is explicitly obtained. If the interaction term is dropped, then one recovers the conventional Mori-Tanaka model. With further approximations, the dilute model and the self-consistent model can also be obtained within the proposed framework. It is observed that the particle interactions make no contribution to the effective bulk modulus, a result that is consistent with other models and experiments for composites with cubic lattices.