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Externally applied unbalanced forces and their corresponding impulses are generally excluded from consideration in regards to the evaluation of the collision phase events for a system comprised of two motor vehicles undergoing collinear impact. This exclusion is generally warranted secondary to the fact that the collision force and its corresponding impulse are dominant during the collision phase. Conceptually, two exclusions exist to this approach. The first is the situation in which significant physical restraints are present to the displacement of one or both collision partners and are of sufficient magnitude as to require inclusion. Generally, this represents the exceptional case and includes, but is not limited to, situations in which one vehicle is snagged, in a non-eccentric manner, by a rigid narrow-width object such as a pole or other similar restraint, prior to the occurrence of the subsequent vehicle-to-vehicle collision under evaluation.

The subject study is the first in a multi-part study that assesses the effects of vehicle planar geometry model non-orthogonality within the context of the constant stiffness force-crush model. The concept of the crush space is first developed. It is shown that under the constraints of the constant stiffness force-crush model that regardless of the complexity of the undeformed vehicle geometry that the crush space is orthogonal and the mapping of vehicle crush into this space retains this orthogonality. Closed form analytical solutions are developed for the mapping of vehicle crush for simple multilinear approximations, the general multilinear approximation and simple circular segment model. Included in this development is the use of measurements taken with respect to a reference plane or line that is parallel to one of the undeformed vehicle principal axes.

The subject theoretical study was undertaken with the purpose of determining the replicability, using a mechanics of materials approach, of the energy absorbed term associated with the B stiffness coefficient of the empirical constant stiffness force-crush model. For the non-restitutive case, it is shown that this term can be derived exactly using a plane rectangular bilinear element formulation with appropriately prescribed nodal displacements and a constitutive formulation based on the linear isotropic model but with the enforcement of zero values for both the shear modulus and the Poisson's ratio. The analytical closed-form solution for the non-restitutive plane stress model with two translational degrees of freedom per node coupled with a fully developed linear elastic formulation is also derived. An example is included to show the implementation of these models.

The subject study presents the results of an investigation into the effects of the level of mesh fineness used on the calculated test vehicle b1-Campbell and CRASH3 A and B stiffness coefficients based upon FMVSS 214D compliance and high-speed lateral NCAP assessment tests. An analytical method is presented based upon a matrix implementation of the existing CRASH3 formulation that allows for the rapid evaluation of all iterations of the equally spaced formulation based on the number of measured crush values present to the front face of the side-impact moving deformable barrier {N: 2 ≤ N ≤ 17}. This formulation accounts for the necessity for aligning the nodes used in the discretization of the direct damage regions of the test vehicle and the moving deformable barrier for the zonal implementation of the force balance method.

In accident reconstruction, parameters such as the struck vehicle change in speed and the closing speed can usually be determined by means of conservation of energy and conservation of momentum approaches. While others have considered limiting cases of the effects of mass and stiffness on vehicle speed change and closing speed calculations, the full spectrum of variations in vehicle stiffness and mass ratios have not been rigorously evaluated. This paper presents a discussion of the effects on the calculated vehicle speed change as a function of the variation of the mass and stiffness ratios. Closed form analytical solutions and graphical representations are derived and depicted for the situations in which the ratio of the barrier impact test masses equate to that of the ratio of the vehicle masses for the reconstructed situation in question and for the scenario in which they do not.