最小化有限黏度可增强双稳态机械超材料中的相对动能吸收，但仅在足够精细的离散化下成立：一种非线性动力学尺寸效应
Minimizing finite viscosity enhances relative kinetic energy absorption in bistable mechanical metamaterials but only with sufficiently fine discretization: a nonlinear dynamical size effect
AI总结：
本文通过数值模拟研究一维双稳态机械超材料在高速冲击下的动力学响应，发现仅在足够精细离散化且黏度有限较低时，其峰值动能吸收性能可显著优于线性系统，揭示了非线性动力学尺寸效应。
摘要：
双稳态机械超材料通过将动能转化为储存的应变能，在减轻冲击有害后果方面展现出前景，为传统能量传输衰减方法提供了一种替代且可能具有协同作用的途径。在本工作中，我们数值研究了一维双稳态超材料受到高速冲击物撞击（冲击物速度与声速相当）时的动态响应，采用的性能指标为超材料中点处经历的峰值动能与一个在其他方面完全相同的线性系统中的峰值动能之比。我们得到五项关键发现：1）随着黏度降低（但仍保持有限），双稳态材料可以反直觉地表现得更好（比线性系统好近1000倍），但仅在达到足够精细的离散化时（即系统足够接近连续极限）才成立；2）该离散化阈值是急剧的，并且取决于所存在的黏度；3）双稳态材料也可能表现得明显比线性系统差（在低离散化和低黏度或零黏度情况下）；4）对离散化的依赖性源于能量被分配为孤波列，其脉冲长度与单胞尺寸成正比，其中在存在格点间黏度时，孤波列会诱发高速度梯度，从而与线性材料以及低单胞数双稳态材料相比产生增强的阻尼；5）当在低黏度下达到足够精细的离散化时，双稳态系统在广泛的冲击物条件下都优于线性系统。第一点尤为重要，因为它表明存在一种非线性动力学尺寸效应，即给定某一厚度的保护层……
英文摘要：
Bistable mechanical metamaterials have shown promise for mitigating the harmful consequences of impact by converting kinetic energy into stored strain energy, offering an alternative and potentially synergistic approach to conventional methods of attenuating energy transmission. In this work, we numerically study the dynamic response of a one-dimensional bistable metamaterial struck by a high speed impactor (where the impactor velocity is commensurate with the sound speed), using the peak kinetic energy experienced at midpoint of the metamaterial compared to that in an otherwise identical linear system as our performance metric. We make five key findings: 1) The bistable material can counter-intuitively perform better (to nearly 1000x better than the linear system) as the viscosity decreases (but remains finite), but only when sufficiently fine discretization has been reached (i.e. the system approaches sufficiently close to the continuum limit); 2) This discretization threshold is sharp, and depends on the viscosity present; 3) The bistable materials can also perform significantly worse than linear systems (for low discretization and viscosity or zero viscosity); 4) The dependence on discretization stems from the partition of energy into trains of solitary waves that have pulse lengths proportional to the unit cell size, where, with intersite viscosity, the solitary wave trains induce high velocity gradients and thus enhanced damping compared to linear, and low-unit-cell-number bistable, materials; and 5) When sufficiently fine discretization has been reached at low viscosities, the bistable system outperforms the linear one for a wide range of impactor conditions. The first point is particularly important, as it shows the existence of a nonlinear dynamical size effect, where, given a protective layer of some thickness...
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