Collision between mass-spring systems

As an effective simplification of beam-on-beam collision problems, a mass-spring model is proposed and analyzed. The energy partitioning between the two beams predicted by the mass-spring model very well approximates the rigid-plastic complete solution. Moreover, due to its simplicity and analytical solvability, the mass-spring model serves as a simplest collision system that provides the fundamental features of a structural collision event. In general, a structural response to impact can be divided into two stages: a very brief collision stage, followed by the structural deformation stage. The first stage starts with a severe velocity discontinuity in the contact region, and characterized by the local velocity change and the local contact dissipation. In the second stage, a restoring instant exists at which the stronger structure transfers from an energy dissipation state to a non-dissipation state and the total energy dissipated by this structure is termed the restoring energy. The remaining kinetic energy after this restoring instant will completely be dissipated by the weaker structure, if it exhibits no deformation-hardening. For the structure with constant load-carrying capacity during its large plastic deformation, the initial velocity will not affect the energy partitioning; while the increase of the relative mass of the impinging structure will make the energy-partitioning pattern closer to an elementary static estimate, that is, the structure with lower strength will dissipate all the input energy.