Use of a damped Hertz contact model to represent head impact safety tests

Abstract

Head impacts tests are conducted as part of many types of safety testing, with applications including vehicle crashes, helmets and sports surfaces. A common measure of head injury in these tests is the Head Injury Criterion (HIC), which is calculated from the measured acceleration of a headform during the impact. In this paper, these headform impacts are represented by a Hertz contact model to which a damping term has been added. A power law relationship was found to be appropriate for modelling the effect of headform mass and impact speed on HIC and peak displacement. It was found that the stiffness and damping in the model did not affect the exponents in the power law, but the exponent of displacement in the contact model did have an effect on all of the exponents in the power law. This result may explain why some variation exists in real data. The relationships presented in this paper may be used to predict how the HIC and maximum displacement of the head will vary for a given change in head mass or impact speed. This has applications in test protocol development and for evaluating the safety performance of tested structures under a variety of real world conditions.