LPV type model of deformational force in vehicle collisions
The CRASH3 computer program increasingly is being used by engineers as a tool to reconstruct automobile accidents. The damage analysis portion of CRASH3 provides a useful means for quantifying the change of velocity, ∆V , that was experienced by a vehicle during the collision phase of a traffic accident. The degree of usefulness of the damage analysis portion of the program, however, is dependent upon the availability of valid crush stiffness coefficients. Published crush stiffness coefficients are available for a large number of vehicles  & . These publications, however, contain only a limited number of coefficients that describe the stiffness characteristics of the side structure of vehicles. Engineers are often asked to perform an accident reconstruction when there are neither published stiffness coefficients for the side structure of an involved vehicle nor crash test data from which to determine the stiffness. Such a collision usually involves the front end structure of a striking "bullet" vehicle and the side structure of a left turning "target" vehicle. If stiffness coefficients are available for the bullet vehicle, then it may be possible to determine accident-specific stiffness coefficients for the target vehicle. A method is presented in this paper that will allow a determination of accident-specific crush stiffness coefficients for target vehicles. The method is based in theory on the CRASH3 damage algorithm. Intrinsic to * The numbers in the brackets refer to references listed at the end of the paper. the CRASH3 damage algorithm is Newton's Third Law of Motion that states that the forces of action and reaction between interacting bodies are equal in magnitude, opposite in direction and collinear. The collision force exerted on the bullet vehicle is calculated based upon its known stiffness characteristics and the magnitude of its residual crush. The collision force exerted on the target vehicle is set equal to the calculated collision force of the bullet vehicle. Next the damage offset speed, b0 , of the target vehicle structure is estimated. An estimation of the damage offset speed is required when mathematically determining the CRASH3 stiffness coefficients, A and B . The estimated damage offset speed is then used, with the calculated collision force, to determine the accidentspecific stiffness coefficients of the target vehicle. "Hard spots" such as wheel assemblies can be taken into account during this estimation. The stiffness coefficients determined by this method will be based on the complex circumstances of the specific traffic accident. As a result, the stiffness coefficients determined for target vehicles involved in different accidents may not be based on a common and/or constant set of parameters. These stiffness coefficients, therefore, should be considered valid only for the specific accident.