Analytical Approach: Collision Routine

Typical Impulse-Momentum analyses of the collision phase (e.g., ref. 2-5) do not yield information on the magnitudes of forces and the extent of damage is generally not included, except for the case of full width frontal or rear contacts (ref. 6). In the development of SMAC, it was considered highly desirable to devise a means of analytical generation of damage patterns for comparisons with corresponding measurements of the damaged vehicle. Therefore, a major effort was applied to development of an analysis that includes an approximation of vehicle crush properties.

Within the research program described in Ref. 7, it was found that crush properties of the peripheral structures of automobiles could be approximated with a reasonable degree of accuracy by means of the assumption of a layer of isotropic, homogeneous material that exhibits elastic-plastic behavior. Comparisons of deformations and deceleration measured in full frontal contacts (ref. 6) indicate a general agreement in the required properties for such an assumed peripheral layer.

In the SMAC collision calculations, the specific crush properties that are assumed do not, of course, affect the conservation of momentum. By producing a finite duration for the application of the forces, the simulated crush permits relative motions of the colliding bodies to occur during the reconstructed collision. The time-varying values for the magnitudes, positions, and orientations of collision forces that are obtained with relatively gross approximations of crush properties have been found to yield results that are more realistic than simple impulse-momentum calculations in which the effects of crush are neglected.

In the SMAC program, the original (undeformed) boundaries of the vehicles are defined in the form of rectangles. Discrete points defining the body outlines in contact regions are generated and displaced during the impact calculations. These points serve to define the deformed boundaries. The distance between a displaced point and the initial boundary of the deflected surface is used to determine the dynamic pressure at that point during any time increment in which the point is displaced. An iterative procedure is used to adjust the displacements to achieve equal pressures from the two mutually deformed bodies at each displaced point, and a point-by-point integration of the pressure on the collision interface is used to generate the resultant collision force and a corresponding inter-vehicle friction force.

The following specific analytical assumptions constitute the basis for the collision force routine of the SMAC program:

The vehicles are treated as rigid bodies, each surrounded by a layer of isotropic, homogeneous material that exhibits elastic-plastic behavior.

The dynamic pressure in the peripheral layer increases linearly with the depth of penetration relative to the initial boundary of the deflected surface.

The adjustable, nonlinear coefficient of restitution varies as a function of the maximum deflection.

The vehicle motions are limited to a horizontal plane in which the effects of pitch and roll are neglected.


Analytical Approach: Tire Forces