Modeling the Effect of Foam Density and Strain Rate on the Compressive Response of Polyurethane Foams

Due to the high deformability and energy dissipation capacity of polymer foams in compression, they are used in automotive applications to mitigate mechanical impacts. The mechanical response of the foams is strongly affected by their density. Phenomenological relations have been proposed to describe the effect of foam density on their stress-strain response in compression at a fixed loading rate and the effect of loading rate at a fixed foam density. In the present work, these empirical approaches are combined allowing for the dependence of loading rate effect in compression on foam density. The minimum experimental data set for calibration of the proposed model consists of compression test results at two different loading rates of foams with two different densities. Rigid closed-cell polyurethane foams with apparent density in the range of ca. 100 to 300 kg/m³ have been produced and tested in compression up to a ca. 80% engineering strain at low (0.00167 to 0.5 s⁻¹) and intermediate (~10² s⁻¹) strain rates. The model parameters were evaluated from test results of the largest and smallest-density foams at low loading rates, differing by two orders of magnitude. The relative root mean square error of stress prediction for intermediate foam densities was found to range from ca. 6 to 12% at low strain rates and reach up to 34% at the higher strain rate. The proposed approach for modeling of foam behavior is expected to be useful in preliminary design of structural parts with impact mitigation functionality.