On the quasi-static and dynamic crushing of random foams

Lightweight cellular materials such as foams exhibit excellent energy absorption characteristics and are widely used for impact mitigation in a variety of applications. In this study a modeling framework is developed in order to investigate the crushing behavior of Al-alloy open-cell foams under quasi-static and dynamic loadings. Quasi-static crushing produces a response that exhibits a relatively stiff linearly elastic regime that terminates into a load maximum; it is followed by an extended load plateau during which localized cell crushing initiates and gradually spreads throughout the specimen. When most of the cells are crushed the densified material stiffens again. Quasi-static compression is simulated using micromechanically accurate foam models. Skeletal random models are generated from soap froth using the Surface Evolver software. The linear edges of the skeletal microstructure are then dressed with appropriate distributions of solid to match those of ligaments in the actual foams and their relative density. The ligaments are modeled as shear-deformable beams with variable cross sections discretized with beam elements in LS-DYNA, while the Al-alloy is modeled as a finitely deforming elastic-plastic material. Utilization of the beam-to-beam contact algorithm of the code is an essential component of the simulation of crushing. Such models are shown to reproduce all aspects of quasi-static crushing faithfully. Dynamic crushing experiments on the same foam have shown that specimens impacted at velocities of 60 m/s and above develop nearly planar shocks that propagate at well-defined velocities crushing the specimen. The same modeling framework is used to simulate these impact experiments. It is demonstrated that random foam models reproduce essentially all aspects of the dynamic crushing behavior observed experimentally. This includes the formation and propagation of shocks, the stresses at both ends, the Hugoniot strain, and the linear relationship of shock front vs. impact velocities. The same models are also used to examine the transition from quasi-static to shock front type crushing. In addition, a detailed parametric analysis is performed to examine the effect of relative density on the crushing response, from the quasi-static initiation and plateau stresses to the formation of shocks and the associated Hugoniot.