Modeling and analytical study of progressive collapse of aluminum foam

Axial compression behavior of foam materials can be explained by two ideal deformation scenarios: discrete crush band process and progressive collapse. In this paper، a perfectly new model for strength assessment and quantitative/qualitative description of one-dimensional progressive collapse of aluminum foams under impulsive loadings is presented and its capability to split this way of crushing into two distinct regimes of shock wave and elastic- plasic wave propagation is highlighted. Then، using conservation relations and the new introduced model، the analytical solution of dynamic deformation of aluminum foams in the two mentioned regimes is developed. Regime 2 considers the case when the crushing front velocity is lower than the linear sound velocity of the foam; but remains higher than the effective sound velocity for a perturbation in which the amplitude lies in the so-called “plateau region’ of the static stress-strain diagram. The physical difference between this regime and the fiest one entails not only the creation a shock front associated with the collapsing foam، but also an acoustic precursor in the case of second regime. Finite element simulation is also performed to validate the analytical procedure. The numerical prediction is found to be in very good agreement with the analytical results.