Stiffness Parameters for Vehicle Collision Analysis, an Update

At the 1991 SAE Congress, a paper entitled "Stiffness Parameters for Vehicle Collision Analysis" was published. The section that attracted the most interest dealt with various methods to relate the CRASH stiffness parameters (A and B) to the SMAC stiffness parameter (KV). The discussion immediately following the paper presentation revealed one more method (developed by Fonda) to relate the CRASH and SMAC parameters consistently with regards to crash energy. These last ten years there have been three significant developments concerning a consistent CRASH-SMAC conversion. Firstly, a greater range of software providers has developed more variations of each basic computer program. Secondly, the CRASH algorithm has been extended so that it treats rebound more like the old SMAC. And thirdly, two completely different versions of SMAC have been released which provide for a bilinear force-displacement curve like the old CRASH. The lack of clarity regarding the various crash algorithms became evident during the 2000 SAE Congress, when a paper was presented which concluded that to achieve consistent results for a crash between two vehicles, the CRASH "A" values for the two vehicles needed to be the same. This paper re-visits the question of how to relate CRASH to SMAC calculations. Because the crash algorithms have become more complicated, the re-visit employs numerical integrations, which were not required for the paper ten years ago. The calculated results clearly show under what conditions the various CRASH and SMAC algorithms will yield consistent results for frontal in-line collisions. A new set of force-crush relations based upon elasticplastic theory is introduced. Compared to previously published force-crush relations, the new one is found to be simpler, easier to handle numerically, and lead to somewhat more realistic crash pulses.