Wave propagation-based characterization of 3D-printed soft auxetic structures

Recent advances in soft mechanical metamaterials, which exhibit unique dynamic behaviors and anti-fragility, have led to the adoption of soft auxetic structures, one of several types of emerging functional structures, step-by-step into practical applications in the electronics, automotive, construction, and robotics fields. However, predicting the dynamic characteristics of soft auxetic structures remains a challenge, which in turn limits their applications due to a lack of comprehensive understanding of the structures. Here, through wave propagation- based theoretical modeling and experiments, a numerical method was presented to evaluate the dynamic properties of 3D soft auxetic structures composed of a viscoelastic polymer. 3D soft auxetic structures with three different unit cell sizes of re-entrant honeycomb were fabricated using a 3D printer. The theoretical procedure for predicting dynamic behaviors of the auxetic structures was presented and verified via comparison with wave propagation experiments. The frequency-dependent wavenumbers of the auxetic structures were derived by the Newton-Raphson method utilizing the predicted and measured transfer functions. The dynamic modulus and loss factor of the auxetic structures were then determined using the wavenumbers. This numerical approach is expected to provide a broader understanding of soft auxetic structures, which will lead to an expansion of the application fields.