Crush Stiffness Coefficients, Restitution Constants, and a Revision of CRASH3 & SMAC 980029

A revision of the modeling of restitution properties in the SMAC computer program and the introduction of restitution properties in the CRASH3 program have been proposed by McHenry [1], the author of M-CRASH and M-SMAC [2]. The accuracy of an accident reconstruction, which uses the proposed restitution model, is directly related to the accuracy of the crush stiffness coefficients employed. The ideal condition for determining crush stiffness coefficients for these programs requires crash tests of a vehicle structure through a wide range of impact speeds with a rigid barrier. Reports from these crash tests should contain the usual data found in NHTSA crash test reports plus rebound velocity and maximum dynamic crush. Unfortunately, such comprehensive tests are very rare. As a result, certain vehicle properties need to be generalized from the existing available crash tests. These generalized properties can then be used to calculate crush stiffness coefficients for these programs.

The revised restitution model extends the original CRASH3 program by accounting for vehicle restitution properties and revises the restitution model of the original SMAC program. The two different force-deflection models used in the original programs are unified into a single force-deflection model. As a result, the revised CRASH3/SMAC would use identical crush stiffness coefficients and restitution constants to describe the crush response characteristics of vehicles.

The restitution portion of the new force-deflection model has an underlying problem. The new force-deflection model coupled with improperly determined crush stiffness coefficients and restitution constants can create vehicle properties that are not realistic. Properly determined coefficients/constants, however, used in conjunction with the revised CRASH3/SMAC force-deflection model should result in improved accuracy over the original CRASH3 and SMAC programs when estimating collision severity.

Set forth in this paper is a method for determining crush stiffness coefficients and restitution constants for the revised CRASH3 and SMAC. Steps are taken to prevent unrealistic modeling of vehicle properties. Finally, this method will provide a means to calculate the coefficients/constants in the absence of comprehensive testing.