Shock Dynamics of Architected Materials

Recent advances in additive manufacturing have facilitated the design of novel architected materials that exploit control over material mesostructure, to outperform typical cellular solids and produce effective properties, including stiffness and strength, that often reach theoretical upper bounds. However, the corresponding gains at high-loading rates remain largely unexplored. It has been established that at above a certain critical impact velocity, the compressive deformation of cellular solids changes to a shock-type behavior, with a sharp front forming at the impact plane and subsequently traversing the material. In this regime, the stresses at impact and distal ends are connected through the classic jump conditions of shock physics. We will present numerical and theoretical techniques that aim to quantify the effect of topology on the shock dynamic behavior of architected materials, and in particular on the stress-velocity Hugoniot and associated energy absorption capacity. First, we examine the dynamic response of two architected materials with distinct topologies but sharing the same density and identical quasi-static strength. The results indicate that as the loading rate increases the effect of material architecture decreases significantly. We will also describe ongoing efforts to develop analytical formulas that are able to capture the dynamic stresses of architected materials and the associated Hugoniot curves, by using solely their quasi-static response and the jump conditions connecting mass, linear momentum, and internal energy across the propagating shock.