On the effect of topology on the shock dynamics of architected materials

Lightweight architected materials, such as microlattices and foams, exhibit excellent energy absorption characteristics and are thus excellent candidates in protective structural components against impact or blast loads. It has been established that at a certain critical impact velocity, the compressive deformation of these material systems changes to a shock-type behavior, with a sharp geometric front forming at the impact plane and subsequently traversing the material. In this regime, the stresses at the 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 and in particular the stress-velocity Hugoniot and the energy absorption capacity of architected materials. First, we examine the dynamic response of two architected materials with distinct topologies but sharing the same density and an almost identical quasi-static strength. The results indicate that as the loading rate increases the effect of material architecture decreases significantly. We will also show our efforts in the development of analytical formulas that are able to capture the dynamic stresses of architected materials, and the associated Hugoniot curves, without the use of a homogenized constitutive model.