Evaluation of shock migration performance for a multi-stable mechanical metamaterial

Abstract

Studies on multi-stable metamaterials mainly focus on the quasi-static performance and the viscoelastic properties of the substrate are ignored, which could cause great deviations in shock migration performance evaluation. In the study, a multi-stable mechanical metamaterial prototype with 2 × 4 cells are investigated and fabricated by thermoplastic polyurethanes (TPU). An analytical, experimental and numerical model was developed to evaluate the dynamic characteristics of the TPU substrate from 0.001 s−1 to 33 s−1, which illustrates significant higher stress levels at higher strain rates. A generalized Maxwell viscoelastic constitutive model was constructed for numerical analysis. Experiments involving quasi-static compression and drop-impact were done to evaluate the prototype's energy absorption and shock reduction capabilities. Quasi-static compression tests and simulations revealed that the peak force of the prototype is about 2.20kN, which presented great repeatability at different loading velocities. The prototype showed significant shock mitigation ability, which could reduce shock acceleration amplitude from 147.02 g to 22.54 g. But the peak reaction force obtained through the acceleration response curve was 3.21 kN, which was 50 % larger than those obtained by quasi-static experiments and simulations. Numerical simulation considering viscoelasticity of the substrate could accurately predict the response of this type of prototype with different shock amplitude, which demonstrates an effective method for the design of protective facilities with specified requirements.