Impact response of negative stiffness curved-beam-architected metastructures

Mechanical metamaterials and metastructures exhibit superior effective mechanical properties, such as enhanced energy dissipation and resistance against impact loads, beyond those of natural materials. Metastructures with the ability to manipulate wave propagation are particularly desirable in numerous applications, such as actuators, dampers, and lightweight impact resistant systems with structural tunability and recoverability. Specifically, multi-stable structural forms have attracted considerable attention in the design of architected multi-materials, metamaterials, and morphing structures. To design such systems, a recently developed mechanical metamaterial/metastructure known as negative stiffness honeycomb, composed of arrays of curved double-beams (CDBs), is proposed. Here, we develop an analytical model to predict the dynamic response of the CDB metastructures, architected with a periodic array of the CDBs, and subjected to impact by a striker. The analytical model is developed using the Euler-Lagrange theorem and the snap-buckling phenomena in the honeycomb have been examined. The derived closed-form solutions were in good agreement with those of the numerical finite element model at different bistability ratios, defined as the ratio of beam apex height to its thickness. The findings demonstrated that the bistability ratio had a noticeable influence on the buckling response of the metastructure and the desired negativity in the stiffness matrix, while the snap-back buckling phenomena may be realised at high bistability ratios.