Mathematical modeling of linear viscoelastic impact: Application to drop impact testing of articular cartilage

► Impact testing is considered in the framework of the linear theory of viscoelasticity. ► Exact analytical solutions are obtained for the main parameters of the Kelvin-Voigt and Maxwell impact models. ► Perturbation analysis of the impact process according to the standard viscoelastic solid model is performed. ► Asymptotic solutions are obtained for the drop weight impact test. ► The dependence of the coefficient of restitution on the impactor parameters has been studied in detail.