Topological features dictate the mechanics of the mammalian brains

•The topology of the brain from different species are key to understand brain mechanics.•We use computational models to understand the role of these brain topological features.•The topological diversity in brain models is more important than differences in tissue mechanics.•Topological differences also modify spatial distribution of mechanical variables.•The folding of mammalian brains act as a damping system to reduce mechanical damage in large-mass brain mammals.•A detailed geometric model is key to generate accurate mechanical predictions.