Vehicle crashworthiness performance in frontal impact: Mathematical model using elastic pendulum

Vehicle occupant injuries due to collisions cause many fatalities every year. Safe vehicle design plays a critical role in averting serious injuries to occupants and vulnerable road users in the event of a crash. In this paper we study a full frontal vehicle crash against a rigid barrier introducing a Lumped Parameter Model (LPM) inspired by the elastic pendulum motion. The model uses polar coordinates to simplify the problem and the governing equations have been defined using Lagrangian formulation. The Simulink model has been validated against Finite Element (FE) data demonstrating good correlation with pitching angle and maximum crush of the vehicle. These parameters are crucial for designing vehicles which efficiently protect occupants.