Many neurological disorders require treatment through surgery. However, brain tissue is susceptible to large deformations during such procedures due to its ultra-soft nature. These large deformations could result in damage to the tissue, leading to possible loss of function for the patient. Thus, a thorough understanding of the large-strain mechanical behaviour of brain tissue and the resulting damage is imperative. Therefore, this work presents a hyperelastic damage model for simulating damage to brain tissue, that adapts existing models existing models which have been used to model damage to soft tissue. We designed and performed dedicated compression experiments on porcine brain tissue. The model parameters were then fitted using the experimental data and an inverse parameter identification framework, where the experimental procedure is simulated using the finite element method. The combined experimental and computational modelling approach lays the foundation for the accurate prediction of brain tissue damage, during, for example, open brain surgeries, and the improvement of neuronavigation systems.