Interactions between dark matter (DM) and radiation (photons or neutrinos) in the early Universe suppress density fluctuations on small mass scales. Here we perform a thorough analysis of structure formation in the fully non-linear regime using N-body simulations for models with DM-radiation interactions and compare the results to a traditional calculation in which DM only interacts gravitationally. Significant differences arise due to the presence of interactions, in terms of the number of low-mass DM haloes and their properties, such as their spin and density profile. These differences are clearly seen even for haloes more massive than the scale on which density fluctuations are suppressed. We also show that semi-analytical descriptions of the matter distribution in the non-linear regime fail to reproduce our numerical results, emphasizing the challenge of predicting structure formation in models with physics beyond collisionless DM.

11 pages, 9 figures, 1 table