Numerical results for the axially compressed cylindrical shell demonstrate the post-buckling response snaking in both the applied load and corresponding end-shortening. Fluctuations in load, associated with progressive axial formation of circumferential rings of dimples, are well known. Snaking in end-shortening, describing the evolution from a single dimple into the first complete ring of dimples, is a recent discovery. To uncover the mechanics behind these different phenomena, simple finite degree-of-freedom cellular models are introduced, based on hierarchical arrangements of simple unit cells with snapback characteristics. The analyses indicate two fundamentally different variants to this new form of snaking. Each cell has its own Maxwell displacement, which are either separated or overlap. In the presence of energetic background disturbance, the differences between these two situations can be crucial. If the Maxwell displacements of individual cells are separated, then buckling is likely to occur sequentially, with the system able to settle into different localized states in turn. Yet if Maxwell displacements overlap, then a global buckling pattern triggers immediately as a dynamic domino effect. We use the term Maxwell tipping point to identify the point of switching between these two behaviours.

中文翻译：

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麦克斯韦临界点：轴向压缩圆柱壳的隐藏力学

轴向压缩圆柱壳的数值结果表明，在施加载荷和相应的端部缩短时，屈曲后响应呈蛇行状。众所周知，与凹坑圆周环的逐步轴向形成相关的载荷波动是众所周知的。在末端缩短中蜿蜒，描述了从单个凹坑到第一个完整的凹坑环的演变，是最近的一项发现。为了揭示这些不同现象背后的机制，我们引入了简单的有限自由度细胞模型，该模型基于具有回弹特性的简单晶胞的分层排列。分析表明这种新形式的蛇有两种根本不同的变体。每个单元格都有自己的麦克斯韦位移，它们要么是分开的，要么是重叠的。在存在能量背景干扰的情况下，这两种情况之间的差异可能至关重要。如果单个单元的麦克斯韦位移被分开，那么屈曲很可能依次发生，系统能够依次进入不同的局部状态。然而，如果麦克斯韦位移重叠，那么全局屈曲模式会作为动态多米诺骨牌效应立即触发。我们使用术语麦克斯韦临界点来确定这两种行为之间的切换点。