We present a mathematical model to study the dissipation of energy in a composite helmet that is subjected to blast loading. In addition to assuming a constitutive relation for the material of the helmet, we also assume models for the skull, and brain, all of them being treated as homogeneous isotropic bodies. A rate type model with non-linear dissipative response characteristics is assumed within the context of a thermodynamic framework for the helmet, as well as the skull, and brain. We study the effect of orientation, the region of impact, the dissipative materials used in the helmet, and the interface condition between the helmet and head assembly. We present a numerical simulation corresponding to different dissipative mechanisms that lead to multiple wave transmissions and reflections that could be detrimental to the brain, highlighting the necessity to pick the materials for the helmet with great care. © 2020 Elsevier Ltd