Investigation into the behavior of a graded cellular rod under impact

• Analytical modeling of the cellular foam with density gradient under impact is carried out.
• We find two deformation modes for the graded cellular rod.
• The influences of the gradient on the energy-absorbing capacity and transmitted force are studied.
• Two artificial special cases are investigated to understand the coupled effect of the density gradient.
• Finite element simulations with metal foams confirm the analytical result.

Over the past few decades, functionally graded materials (FGMs) have attracted many research interests. For the cellular material, the variation of the mechanical property may significantly influence the global performance of the structure. Previously the authors have presented the basic deformation patterns in a simple case, in which only the quasi-static plateaus stress gradually decreases or increases along the rod and the density is uniform. In the current study, further investigations are carried out into the effect of the gradient in the initial density, which inherently leads to variation in the quasi-static plateau stress. A simple impact scenario is considered, in which a rigid mass strikes a stationary cellular rod with variation in the initial density of the material. Similar to the previous studies, the rigid-perfectly plastic-locking (R-PP-L) material model and the simple shock theory are employed to carry out the analysis. Current study confirms that the basic deformation modes (i.e. double shock (DS) and single shock (SS) modes) still exist in the cellular rod with density gradient. The analytical results indicate that the negative gradient weakens the capacity of energy absorption while positive gradient has little influence. Then, the effect of the initial density gradient is further investigated by considering two artificial cases with only one gradient either in the quasi-static stress or in the initial density. Finally, finite element (FE) simulations are carried out with practical metal foam in order to verify the analytical modeling.