Recently, multiscale modeling frameworks combining micromechanics-based homogenization methods and atomistic simulations have been widely applied to predict the effective stiffness of particulate-reinforced composites. Although most studies demonstrated that theoretical predictions incorporating interfacial damage are necessary to explain atomistic simulation results, the microscopic origin of the interfacial damage has not been systematically analyzed in terms of interatomic potential and interfacial structure. In this study, first, we conduct a series of particle simulations of two fictitious model crystalline composites with coherent interfaces: one has a two-dimensional triangular structure described by a bead-spring model and the other has a face-centered cubic structure described by the artificial Lennard-Jones potential. By comparing the simulation results with micromechanics theory, we obtain the interfacial bonding (damage) parameter used in the homogenization method in terms of parameters at the atomistic level. Second, we study the effects of the interfacial structures (coherent/incoherent) because of lattice or crystallographic orientation mismatch on the effective properties of composites. We obtain the elastic stiffness of Si(matrix)-Ge(nanoparticle) nanocomposites with different interfacial structures (coherent/incoherent structures) using atomistic simulations and observe that nanoparticle-size-dependency occurs only for the composite with incoherent interfaces. We propose a homogenization scheme considering the pre-stress (or residual stress) and interfacial imperfection, and explain the results from Si-Ge nanocomposite simulations. (C) 2021 Elsevier Ltd. All rights reserved.