Dynamic crushing of aluminum foams: Part II – Analysis

Abstract

Part II of this study uses micromechanically accurate foam models to simulate and study the dynamic crushing of open-cell foams. The model starts as random soap froth generated using the Surface Evolver software to mimic the microstructure of the foams tested. The linear edges of the cellular microstructure are “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. The numerical contact algorithm of the code is used to model ligament contact and limit localized cell crushing. The quasi-static and all dynamic crushing experiments in Part I are simulated numerically. The models are shown to reproduce all aspects of the crushing behavior including the formation and evolution of nearly planar shocks, the force acting at the two ends, the shock front velocity, the strain in the crushed material behind the shock, and the energy absorbed.The transition to shock behavior is rather gradual. At speeds 20m/s and lower all aspects of the crushing replicate the quasi-static behavior. Between 20 and 40m/s inertial effects start to become apparent with a gradual increase in the stress and strain at the proximal end. Shocks were found to occur above impact speeds of 40–50m/s.Models were also crushed at constant velocities up to 200m/s. Different representations of the Hugoniot were calculated and are shown to reinforce the experimentally generated ones in Part I. This includes the linearity of the shock-impact velocities Hugoniot, the asymptotic increase with impact velocity of the strain in the crushed region, and the quadratic increase of the proximal stress with velocity. The results also confirmed that the stress ahead of the shocks is at the level of the limit stress of the quasi-static crushing response.