A theoretical study of shock front propagation in the density graded cellular rods

The present theoretical study focuses on the shock front propagation in a density graded cellular rod. It aims at the determination of the shock front velocity evolution as well as the stress evolution during the impact. The density gradient leads necessarily to the property gradient, which is taken into account in this analysis. The locking strain in classical shock front theory is replaced by the notion of the locking density to adapt to the studied case. Analytical solutions of linear, quadratic and square root density profiles are obtained. They are compared to the FEM solution with a good agreement. This study reveals a possibility to reduce the maximum impact stress for the impacted structures (same impacting mass, same energy absorption) using a proper density gradient.