On the rigid projectile model for low velocity impacts

Most of the studies about low velocity impact aimed to determine the impact force and the impact duration. The influence of the interaction law between the projectile and the target on the response has been examined; the influence of the structure model on the response has been addressed as well. However when the projectile is much more rigid than the structure, it has always been considered as an infinitely rigid mass. This paper shows that such a model tends to overestimate the maximum impact force and underestimate the impact duration; however, a 2-degree-of-freedom (dof) model has been suitable to recover the impact force very well. Moreover, it is shown that this rigid projectile may be viewed as a rigid mass associated with a modified Hertz law. These results have been established for a sphere–sphere impact and a sphere–beam impact as well. Nevertheless, it has been shown that the 1-dof model is definitively relevant to determine the structural response: in fact the displacement of the structure provided by the 1-dof model and the 2-dof model are the same, as indicated in the last section.