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.