An analytical model to study the effective stiffness of the composites with periodically distributed sphere particles

In order to analytically study the overall elastic stiffness of the composite containing periodically dispersed sphere particles, a new micro-mechanics model is developed in this paper. Three kinds of typical particle packing arrangements in the form of simple cubic lattice, body-centered cubic lattice and face-centered cubic lattice are considered and compared. The special characteristics of regular distribution are fully considered by incorporating the necessary geometrical symmetry conditions into strain Green’s function. It is found that particle arrangement obviously affects the macroscopic elastic response of such the kind of composite. Moreover, most of the predictions by the present model are in good agreement with the FEM computations. The effective Young’s modulus of BCC composite the effective shear modulus of SC composite are not in the range of the Hashin–Shtrikman bounds. The present model is also useful to verify some other numerical results mainly obtained by the unit-cell model, for instance, damage variables, matrix plasticity, etc.