Radial and axial inertia stresses in high strain rate deformation of polymer foams

•An analytical solution is developed for radial and axial inertia stresses in foams under impact.•The analytical model includes the effect of material compressibility.•Effects of strain rate ramp-up are discussed in detail.•Limitations associated with sample dimensions are discussed.•Applicability of the model in SHPB impact testing of foams is discussed. Polymer foams are widely used in applications that require impact energy absorption. Experimental characterization of the impact response of polymer foams is challenging. The primary challenges associated with the characterization of polymer foams in high strain rate conditions are the significant effects of inertia and material compressibility. In this work, we develop analytical solutions for radial and axial inertia stresses that develop during high strain rate deformation of polymer foams. The effects of strain rate increase rate, test piece geometry, density, and Poisson's ratio are discussed in detail. We also provide and discuss results from a case study on the impact response of a closed-cell foam subjected to controlled impact loading, focusing on the importance of inertial effects on the characterization of the dynamic stress-strain response. The analytical approach presented in this work facilitates the determination of the concurrent effects of material compressibility and inertia stresses in the dynamic deformation response of compressible materials. [Display omitted]