On the effect of relative density on the crushing and energy absorption of open-cell foams under impact

Abstract

Micromechanically accurate random foams are used to examine the effect of relative density on the crushing response and energy absorption of aluminum open-cell foams for a range of loading rates. Random soap froth microstructures generated with the Surface Evolver software are dressed with shear deformable beam elements with material distribution that mimics measured values. Foam models of relative densities between 3.67% and 10.0% are crushed first quasi-statically and then dynamically in a direct impact setting covering impact speeds that ranged from sub-to super-critical. Under quasi-static crushing, the limit and plateau stresses and the energy absorbed were found to increase linearly with relative density while the densification strains exhibit a modest linear decrease. In the shock regime, for all densities the proximal stresses rise significantly with relative density whereas the distal ones follow the more modest linear increase of the quasi-static limit stress. The Hugoniot strain depends strongly on impact speed approaching asymptotically values corresponding to the densification of the material at the high end. The energy induced to the material as it crosses the shock also increases also parabolically with impact speed. It was further confirmed that given the shock front velocity-impact speed Hugoniot the rest of the dynamic variables for each foam density can be estimated from the fundamental jump conditions for shocks in solids. For all densities examined it was illustrated that the transition from quasi-static to shock behavior is a process that spans several impact speeds. The transitional range moves to moderately higher velocities as the foam density increases.