Characterizing and modeling the wide strain rate range behavior of air-filled open-cell polymeric foam

Air-filled open-cell polymeric foams are widely used for absorbing impact energy under various strain rates. Modeling their compression behavior under large deformation across a wide strain rate range remains a challenge, as the air pressure is dominated by viscous effect or inertial effect at different strain rates. In this study, the compression response of air-filled open-cell polyurethane (PU) foam is characterized across a wide strain rate range from 0.0001 s⁻¹ to 5000 s⁻¹. The plateau stress and energy absorption properties of the foam exhibit a power-law dependency on strain rate, showing lower rate sensitivity at quasi-static rates and increased sensitivity at high strain rates. To describe the observed rate sensitivity variation, the effect of airflow resistance is quantitatively modeled and a visco-hyperelastic constitutive model considering air pressure is developed. It shows that at high strain rates, the air pressure can constitute up to 30 % of the energy absorption contribution while it is relatively negligible at quasi-static strain rates, which significantly amplifies the difference in rate sensitivity between quasi-static and high strain rates. Furthermore, a simplified semi-empirical formula is proposed to rapidly estimate the air pressure in open-cell foams at high strain rates. This formula demonstrates the mechanical response transition from open-cell to closed-cell foams with increasing strain rates. This study is meaningful for understanding the dynamic response and the energy absorption capabilities of air or fluid filled open-cell foam.