A: The SMAC model is a dynamic force/deflection model that includes modeling the restitution. Implementation of collision modeling in the SMAC computer program includes identical loading and unloading load-deflection rates. Therefore the unloading (restitution) phase of the collision was at near peak levels. The effect of partial restoration of the energy at near peak levels is that the SMAC program returns the restitution part of the absorbed energy but it does so with a less-than-actual dimensional recovery. This acts to reduce the duration of the restitution phase which therefore reduces the duration of the overall impact.
See our paper on Restitution SAE 970960, Effects of Restitution in the Application of Crush Coefficients, from the first few pages should provide an explanation:
- The selected analytical approach to restitution at that time (presently retained in both original SMAC and EDSMAC and other clones of SMAC) included the use of extensive simplifying assumptions aimed at reducing the requirements for associated computer memory and logic. In particular, identical load-deflection rates were applied for loading and unloading.The unloading was implemented at force levels close to the peak values The duration of the impact in SMAC is less than measured tests due to the shorter time period for restitution."
- (and we also, of course, compared the two models with full scale test measurements to demonstrate the correlation of the revised model with the restitution measured in full scale tests)
Engineering Dynamics in 1999 made a poor choice as part of their modification EDSMAC4 to try to 'improve' restitution behavior of SMAC by overloading the initial loading portion of collisions in EDSMAC4.
From our 1999 SAE TOPTEC Review: SMAC Computer Program presentation (from CURRENT STATUS part of the presentation) you'll find:
- In 1999, EDSMAC4 claims to include a "more realistic modeling of actual vehicle structural behavior" based on "an A, B stiffness model". Please note that the "A,B stiffness model" is a "virtual" model equating residual crush to dissipated kinetic energy. The "A,B stiffness model" was not intended to be a dynamic model. With the "A,B stiffness model" a very stiff near plastic vehicle can share the same "A,B stiffness" as a very soft near elastic vehicle. The residual crush on a vehicle does not tell you anything about the vehicle stiffness EXCEPT in the case of a plastic vehicle. Motor vehicles crushing in collisions are not plastic. They have restitution.
Restitution consists of two separate aspects:
- (1) a partial dimensional recovery and
(2) a partial restoration of kinetic energy.
In our 1997 SAE paper on restitution, we pointed out that the current implementation of collision modeling in the SMAC computer program includes identical loading and unloading load-deflection rates and that the unloading (restitution) phase of the collision was at near peak levels. The effect of partial restoration of the energy at near peak levels is that the SMAC program acts to return part of the absorbed energy but it does so with a less-than-actual dimensional recovery.
EDSMAC4 includes in the "A,B stiffness model" a "threshold force to be applied before deformation begins". What mechanism exists in the real world which provides a force without a deflection? Are they assuming that the bumper is a pre-loaded spring? You have to do work to absorb energy in the vehicle structure. Work equals Force * Displacement. The effect of the changes in EDSMAC4 is that the acceleration peaks are higher and the duration of the impact impulse is shorter.
EDSMAC4 has chosen to artificially stiffen the vehicle to try to better match the residual crush. In effect they have created a "residual crush" stiffness model which reduces the validity of the modeling of the loading phase of the collision.
- The most important aspect of a collision is the loading phase.
- (1) a partial dimensional recovery and
What they don't show is that the crash test measurements during loading are more accurately modeled by the original SMAC model (EDSMAC and other clones, the dashed line).
- The EDSMAC4 modifications act to further REDUCE the collision duration and increase the maximum acceleration over original SMAC (EDSMAC) and therefore reduce the correlation with actual test measurements