Refinement in the Simulation of Structural Interactions During Collisions
The interactions between the structures of colliding vehicles that are simulated by the original SMAC and the EDSMAC computer programs are limited to compressive forces and simple Coulomb friction. In many real-world collisions, the actual interactions are much more complex. They frequently include tensile forces and/or momentary interlocking of the structures. In those cases where acceptable matches of the positions and orientations at rest cannot be achieved with the original SMAC and/or the EDSMAC program and, further, where there are no obvious obstacles and/or topographical features that have significantly affected the vehicle motions, it becomes obvious that the simulated vehicle interactions are overly simplified. The SNAG routine of the M-SMAC computer program provides a capability for achieving higher fidelity matches of the positions and headings at rest while maintaining the principles of conservation of linear and angular momentum.
The SNAG routine incorporates impulsive linear and angular constraints that momentarily resist relative motions of the two vehicles while continuing to conserve both the linear and the angular momentum of the two-vehicle system during the collision. By this means, it is possible to simultaneously refine the matches of the positions and headings of both vehicles at their rest positions with a series of iterative adjustments of the impulsive constraints. The rationale of the analytical approach is the concept that inappropriate inputs for the impulsive constraints cannot achieve acceptable responses of both vehicles.
The moment constraint is applied in the form of equal and opposite couples that resist relative rotations of the two vehicles (i.e., it is independent of the locations of application on the two vehicles). The linear constraint also produces moments (generally unequal) on the two vehicles by virtue of the fact that it resists relative movement between specific points on vehicles #1 and #2. The selected point on vehicle #1 is specified in the SNAG inputs and the corresponding point on vehicle #2 is defined as that which coincides at the start of SNAG. Thus, the effective resistance moments on the two vehicles are determined by the algebraic sum of those produced by the moment and the linear constraints.
In applications of M-SMAC, a best effort reconstruction without SNAG should first be attempted. If the achieved matches of the positions and headings at rest of the two vehicles are not acceptable and there are no obvious obstacles and/or terrain features that have affected the motions of one or both vehicles, application of the SNAG routine should be considered.
In an application of SNAG, a linear constraint resisting relative motions should first be applied, starting in the range of 500 to 1000 LB-SEC. The location of the linear constraint on vehicle #1 should correspond to either a major structural component, such as a wheel, or to a damage area that may have generated tensile forces. The objective of the constraint is to modify the rotational (i.e., yaw) responses of the vehicles to more closely match the headings of the two vehicles at rest. If excessive relative rotation occurs, the moment constraint should also be applied. By means of a series of iterative adjustments of the SNAG inputs, the overall match of rest position evidence can generally be improved.
Care must be exercised in selecting the magnitudes of inputs for the constraints and for the corresponding null bands in SNAG to avoid oscillatory behavior. The time-history outputs should be carefully checked for oscillations prior to accepting the results.
It can be demonstrated, by setting the tire/terrain friction coefficient to 0.001, that the SNAG routine does not change the linear or angular momentum of the two-vehicle system during the collision, including the time of application of the constraints that resist relative motions. Thus, improvements in the overall match of the rest position evidence over that achieved with original SMAC and/or EDSMAC, can generally be obtained without any compromise of the validity of the reconstruction technique.
DISCUSSION: Pole Impacts