On the crushing of polydisperse foams

Open-cell low-density foams are widely used in energy absorption and impact mitigation applications because of the low stress crushing response that extends to strains of 50-60%. In a continuing effort to connect the microstructure to these unique properties, we use micromechanically accurate foam models of the same relative density to examine the effect of cell-size distribution (polydispersity) on the full crushing response of aluminum open-cell foams under both quasi-static and dynamic loadings. A foam model starts as a Laguerre tessellation originating from a dense packing of polydisperse spheres with prescribed probability distributions of radii. The tessellation then becomes the initial condition in Surface Evolver to generate soap froth that satisfies Plateau's laws. Such soap froths are subsequently “dressed” with the desired solid material and discretized with finite elements to create foam models of different polydispersity levels. Quasi-static simulations show that the limit stress decreases with increasing polydispersity while the plateau stress is less affected and governed by the relative density, which in this case remains constant. Foams of different polydispersity were also crushed by impact under a range of super-critical speeds. The Hugoniot of a highly polydisperse foam is reported and is compared to the corresponding one of a monodisperse foam of the same density. The results indicate only a modest variation of the shock kinetics with polydispersity, but a drop is recorded in both the distal and proximal stresses, as well as the associated energy absorption capacity of the foam.