Multifunctional Optimization of Viscoelastic Materials Subjected to Spherical Impact

The event of rigid solids impacting a viscoelastic body is encountered in many engineering disciplines. However, for this problem no analytical solution is available, making the proper design of, e.g., protective bodies a difficult task. As a remedy, generally valid solutions in form of nondimensional response curves are presented in this paper, serving as reference for validation purposes or as design charts for the performance-oriented development of impact absorbers. Hereby, the problem of a frictionless rigid sphere impinging a viscoelastic half-space is investigated by finite-element analyses. The general applicability of the results is assured by a transformation to dimensionless problem parameters. For this purpose, the analytical solution by Hertz (1881, "Über die Berührung fester elastischer Körper," J. die Reine Angew. Math., 1882(92), pp. 156-171) for the purely elastic impact is taken into account. The chosen nondimensional format leads to a reduced number of system parameters, allowing for a compact representation by so-called master curves. From these, optimal material characteristics are found for three different design objectives.