A predictive model for impact response of viscoelastic polymers in drop tests

We show for the first time that a classical Hookean viscoelastic constitutive law for rubbery materials can predict the impact forces and deflections measured with a commercial drop tester when a mass, or tup with a flat impacting surface is dropped onto a flat pad of commercial impact-absorbing rubber. The viscoelastic properties of the rubber, namely the relaxation times and strengths, are obtained by a standard rheological linear-oscillatory test, and the equation of momentum transfer is then solved, using these measured parameters, assuming a uniaxial deflection of the pad during the impact. Good agreement between measured and predicted forces and deflections is obtained for a series of various drop heights, tup masses, impact areas, and pad thicknesses, as long as the deflection of the pad relative to its thickness is small or modest (<50% or so), and as long as the area of the pad is less than or equal to that of the tup. When the pad area is greater than the tup, forces are higher than predicted, unless an empirical factor is introduced to account for the nonuniaxial stretching of the ring of material that extends outside of the impact area. These results imply that the impact-absorbing properties of a rubbery polymeric material can be assessed by simply examining the material's linear viscoelastic spectrum.