A key aspect of accident reconstruction is the calculation of how much kinetic energy is dissipated as crush. By far the most widely used methods are derivatives of Campbell’s work, in which a linear relationship between residual crush and closing speed is shown to imply an underlying linearity between force and crush. “Consant-stiffness model” is the term used for such a representation of structural behavior.
Difficulties arise, however, when significant non-uniformities are present in the crush pattern (as in narrow-object and/or side impacts, for example). The term “residual crush” becomes more ambiguous. Do we mean maximum crush, area-weighted average crush, or some other measure of residual deformation? And is it sufficient to represent the non-uniform crush pattern by a single parameter?
Such considerations led to a re-development of the fundamental structural models, with an eye to determining whether the classical constant-stiffness model is the most appropriate. For narrow-object side impacts, a constant-force model was developed. For wide-object impacts, constant-stiffness and constant-force models were developed, along with a three-parameter model.
These models were applied to published side impact and narrow-object data. The constant-force model emerged as the preferred formulation for narrow-object side impacts, and was at least on a par with the constant-stiffness model for wide-object side impacts. For frontal impacts, wide-object test data could not predict narrow-object behavior with acceptable results.