Two widely used computer programs developed for the analysis of vehicle collisions are CRASH and SMAC. This paper reviews stiffness parameters which are used in the application of these programs, and methods to select these parameters. The paper also introduces a rational method to select stiffness parameter KV for the SMAC program.
The CRASH program expresses the vehicle force-crush relationship as FC = A + B*CR, where FC is the force per unit width, and CR is the vehicle residual crush. The “stiffness parameters,” A and B, define a linear relation with a zero-crush intercept. For collinear impacts, these parameters are used in determining crush energy, which in turn is used in determining changes in velocities of the impacting vehicles.
Over the years, considerable effort has been expended by numerous researchers to determine A and B for a variety of vehicles, and a substantial body of vehicle crash test data has been developed and analyzed to this end.
The SMAC program permits time-history dynamic analyses of vehicle collisions. It expresses the vehicle force-deformation relationship by the linear equation, FS = KV*CT, where FS is the force per unit width, KV is the stiffness parameter, and CT is the vehicle total crush. The KV stiffness parameter is usually varied for different vehicles or different classes of vehicles, and, as shown in this paper, should also be varied as a function of vehicle crush.
The method suggested in this paper for the selection of KV is based on 1) the premise that the analyst accepts the vehicle force-crush relationship FC = A + B*CR, and 2) the idea that KV should be chosen such that the crush energies under the force-deformation curves FC and FS are equivalent. This approach allows the SMAC stiffness calculations to benefit from the extensive database of A and B parameters that has been collected. In addition, the method provides a rational basis for selection of stiffness KV that is dependent on crush distance.