Mathematical model of a head subjected to an axisymmetric impact.

Abstract An improved mathematical model is derived which predicts more closely the response of a head to an axisymmetric impact. The three-dimensional equations of linear viscoelasticity are used to describe the behavior of both the brain and the skull. Responses of both human-sized and small animal heads are calculated for steady-state and for transient loadings. An explicit formula is derived for scaling experimental data on contre-coup damage from laboratory animals to humans. General agreement is found between the predictions of the model and observation, with regard to the location and the nature of possible damage. However, before the model can be used to make satisfactory quantitative predictions of the severity of injury, additional empirical data are required on both damage criteria and the mechanical behavior of the brain and skull.