The choice of boundary conditions used in multiscale analysis of heterogeneous materials affects the numerical results, including the macroscopic constitutive response, the type and extent of damage taking place at the microscale and the required size of the Representative Volume Element (RVE). We compare the performance of periodic boundary conditions and minimal kinematic boundary conditions applied to the unit cell of a particulate composite material, both in the absence and presence of damage at the particle–matrix interfaces. In particular, we investigate the response of the RVE under inherently non-periodic loading conditions, and the ability of both boundary conditions to capture localization events that are not aligned with the RVE boundaries. We observe that, although there are some variations in the evolution of the microscale damage between the two methods, there is no significant difference in homogenized responses even when localization is not aligned with the cell boundaries.