Strongly interacting dark matter and the DAMA signal

We show that models of strongly interacting (SIMP) dark matter built to reproduce the DAMA signal actually cannot account for its time dependence. We discuss the constraints on this type of models coming from direct detection experiments and study the propagation of thermalised dark matter particles in the ground for the allowed values of the parameters. We consider a simple 1D diffusion and a more detailed 3D diffusion. In both cases the predicted signal has either the wrong phase of the annual modulation or a much larger amplitude of the diurnal modulation.