The calculation of crush energy for reasonably uniform crush shapes, as detailed by K.L. Campbell, is well understood. Difficulties arise, however, when significant non-uniformities are present in the crush pattern (as in narrow-object and/or side impacts, for example). The "residual crush" term becomes more ambiguous. Does this 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 redevelopment 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 behaviour with acceptable results.
Abstract