Force transmission and dissipation in dynamic compression of architected metamaterials

Materials engineered with an internal architecture in order to achieve unusual properties, so-called mechanical metamaterials, are a promising candidate in the ongoing quest for lightweight impact mitigation. During impact events, these materials are subject to high strain rates, and the forces occurring due to the deceleration of the impactor are transmitted in a non-uniform way. The prevailing research in the field of impact mitigation focuses largely on the global effects of architected materials, with less attention being paid to the internal mechanisms of these structured materials. While there have been recent studies on the distribution of forces throughout an impact event, less research is devoted to the transmission of forces and the distribution of energy dissipation. The objective of this study is to examine the transition from static deformation patterns to dynamic phenomena for different types and sizes of microstructure, and to understand both the force transmission through the patch and the energetic distributions in different strain rate regimes. To enable this investigation discretized---geometrically as well as materially---nonlinear Timoshenko-Ehrenfest beams are used in implicit and explicit finite element schemes. The transmitted force levels and energy dissipation are investigated for two auxetic architectures (one for each mechanism resulting in a negative Poisson's ratio) and one non-auxetic architecture. The dynamic force levels transmitted to the back face exhibit an initial peak of a similar magnitude for all investigated strain rates and stabilize to the static stress plateau for each architecture. While the global amount of potential energy remains largely unchanged for all investigated rates, the amount of dissipation and kinetic energy demonstrates a non-linear increase from static deformation to slow and high rate deformation. The phenomena observed in different architectures are highlighted, and the differences are explained and related back to the configurations of the lattices. Notably, the prevalent notion in literature asserting the superiority of negative Poisson's ratio materials for impact mitigation applications is not replicated in this study.