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Physics and rate dependence of impact energy absorbing bistable mechanical metamaterials


Mechanical impact, long studied, has the power to be harnessed for the positive benefit of society, but clearly can also result in unwanted destruction. Despite centuries of study, there is still much to be learned, particularly as a result of novel materials requiring rigorous analysis to understand both strengths and shortfalls. Metamaterials are a class of material where generally abnormal properties are realized primarily as a result of their internal structure. The study herein focuses on the analysis of a particular mechanical metamaterial design, in which individual "unit cells" making up the broader material exhibit two stable states at zero force on a force versus displacement curve. These "bistable mechanical metamaterials" have received attention due to their ability to elastically "trap" energy, providing an additional and potentially complementary mechanism to more traditional processes to abate energy transmission. The author, through simulation and experiment, analyzed kinetic energy (KE) transmission after impact in a particular bistable mechanical structure, which was compared to the KE transmission of a control material, in order to assess performance. The analysis assumed operation within: the elastic regime, with sample strain rates less than 100 1/s and no plastic effects; "wave-dominated" regimes, wherein the dominant wavelength of the impact pulse is smaller than the overall tested sample size; and regimes where continuum approximations are appropriate, such that the dominant wavelength is larger than the individual unit cell size. Nominal impactor conditions (mass and velocity), hypothesized to result in good performance were estimated, then the sample was subjected to multiple combinations of, primarily simulated, impactor mass and velocity to observe performance differences. Similar trials were conducted with varied unit cell size (in a finite sample size), damping, and unit cell constitutive response. The following novel points were discovered. Performance of the bistable mechanical metamaterial is highly dependent upon the: 1) impact conditions (both impactor mass and velocity), 2) amount of material damping, and 3) number of unit cells within a finite sample size. Additionally, it was observed that alteration of the force versus displacement curve (modeled as a continuous polynomial function) such that the post-buckled stiffness was less than the pre-buckled stiffness improved the maximum performance of this system further, as expected based on prior literature results. These key results, and others herein, represent a small advancement that provides further insight to the suitability and further design of bistable mechanical metamaterials for impact.

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