LAUSR

Abstract Damping is an important parameter to measure the energy dissipated by a cushion foam during an impact. Damping is commonly characterized by damping indices such as damping ratio, loss factor, and tangent of the phase lag. In general, these indices are defined based on steady-state harmonic oscillations of a single degree of freedom, linear viscoelastic model, with an inertia and low damping. When any of these assumptions are violated, the simple linear relationships relating the different damping indices are no longer valid. A steady-state linear model is not well suited for describing impact damping of nonlinear cushion foams. This study reviews classical damping theory and linear and nonlinear viscoelastic models, and proposes a contact force law based nonlinear viscoelastic model for modeling drop platen tests (impact) of a cushion foam. Based on this nonlinear model, a mathematical relationship between the specific damping capacity and damping ratio is formulated. Drop platen tests were carried out under different loading weights and drop heights. The raw data were channeled into dynamic force-deflection curves for calculating analytically specific damping capacity and impact damping ratio. The raw data were also imported into Matlab to develop the numeric impact model for calculating the impact damping ratios. The results show that the nonlinear viscoelastic model, both analytic and numeric, yield damping ratios that are 3–5 times larger than the linear viscoelastic model. The proposed nonlinear viscoelastic model is shown to be an effective tool to describe impact damping and cushion characteristics of a polymer foam. For cushion design, damping ratios of a nonlinear cushion foam are affected by loading weight and strain rate. In addition, the analytical computation of damping ratio, ζ, from specific damping capacity, D, opens up the possibility to project impact damping ratios based on quasi-static compression tests.