Gilbert, B., Jadischke, R., and McCarthy, J., "Calculating Non-Linear Frontal Stiffness Coefficients," SAE Technical Paper 2014-01-0474, 2014, doi:10.4271/2014-01-0474.
The analysis and modeling of vehicle crush in accident reconstruction has traditionally been based upon the use of linear crush-based, stiffness coefficients. Engineering Dynamics Corporation (EDC) created the accident reconstruction software Human-Vehicle-Environment (HVE) which contains the collision algorithm called DyMESH (DYnamic MEchanical SHell) which is capable of utilizing a non-linear stiffness coefficient model. The objective of this research was to develop an improved methodology for the calculation of non-linear stiffness coefficients.Stiffness coefficients are used to represent the relationship between the impact force on a vehicle and the resulting vehicle crush. The method explored in the present research was focused on developing vehicle specific, non-linear stiffness coefficients (Pressure Model) based upon frontal crash tests into a fixed, rigid barrier equipped with load cells.The load cell data from the barrier and the accelerometer data from the vehicles were used to establish a force per unit area (pressure) versus vehicle displacement (deflection) relationship. The area used in this calculation was based on the actual cross-sectional area of the vehicle for specific depths of crush. The pressure-deflection relationship was fitted using 3rd order polynomial equations. This methodology allowed these frontal stiffness coefficients to be used in the HVE-DyMESH collision algorithm.The accuracy of the non-linear stiffness coefficients was evaluated by comparing output results from HVE-DyMESH for various parameters. These parameters included delta-V, peak force, peak acceleration, crush depth, force versus time graphs, as well as acceleration versus time graphs.The greatest advantage of using a non-linear pressure model was a stronger correlation to the crash tests over a wide range of impact severities. Additionally, the length of the crash pulse increased substantially, providing improved correlation with the actual crash pulse. This is beneficial when trying to establish a crash pulse for use in occupant simulation.