Ratio of Loss and Storage Moduli Determines Restitution Coefficient in Low-Velocity Viscoelastic Impacts

Abstract

Impact tests are an important tool to analyze dynamic material properties of viscoelastic media in technology and biology. In this context, rigorous contact mechanical models of the collision problem are necessary to adequately interpret data from impact experiments. It is shown here theoretically that the coefficient of restitution in these types of testing is mainly a function of one specific material property, namely, the ratio between the loss and storage moduli of the viscoelastic probe at the characteristic timescale of the impact. Explicit dependencies of the restitution coefficient on factors like impact velocity, impactor shape, general material rheology, and functional grading—beyond the fact that those may influence the impact duration and the dynamic modulus associated with it—are weak.