利用翻转屈曲实现理想的全方位能量吸收
Eversion Buckling of Toroidal Shells: Mechanism, Bifurcation, and Applications in Energy Absorption
AI总结：
本文研究了翻转屈曲机制，通过分析膜能与弯曲能的比值，揭示了轴对称构型在不同几何条件下稳定性转变的机制，并通过有限元模拟和实验验证了该机制在设计具有鲁棒性和方向不敏感性的壳体系统中的应用。
摘要：
薄壳体的形状变化受弯曲能与膜能之间的竞争所支配。本文识别了翻转的环形壳体中的一种不稳定性机制，称为翻转屈曲。在翻转后，轴对称构型可能保持稳定或通过对称性破坏失去稳定性，这取决于几何形状。通过缩放分析，发现了一个无量纲参数，该参数表征膜能与弯曲能的比值。该参数定义了一个临界阈值，将双稳态区域（轴对称翻转状态持续）与单稳态区域（壳体坍缩成非轴对称构型）分隔开。该转变与pitchfork型分岔一致，导致坍缩而不具有首选平面方向。有限元模拟和实验验证了所提出的缩放关系和相关稳定性边界在不同壳体几何形状下的适用性。在双稳态区域中，单个翻转壳体表现出快速的 snap-through，伴随大的体积收缩，并且临界响应对边界约束具有有限的敏感性。基于该机制，由此类壳体组成的系统形成具有稳定应力平台和高能量吸收效率的颗粒系统。这些结果为设计具有鲁棒性和方向不敏感性的壳体系统提供了基于力学的框架。
英文摘要：
Thin shells can store and release elastic energy through large geometric transformations, but their post-deformation stability is often highly sensitive to geometry and loading direction. Here, we study the eversion of open toroidal shells generated by revolving a meridional arc about an external axis and identify a geometry-controlled instability, which we define as eversion buckling. After eversion, the shell may either remain in an axisymmetric everted state or spontaneously collapse into a non-axisymmetric configuration. We show that this transition is governed by the competition between bending and membrane energies. A scaling analysis leads to a dimensionless geometric parameter that predicts the onset of eversion buckling, namely, the spontaneous loss of stability of the axisymmetric everted configuration after unloading. Finite element simulations and experiments confirm that this parameter collapses the stability data for shells with different geometries, including circular and semi-elliptical generating curves. The loss of axisymmetric stability is consistent with a pitchfork-like symmetry-breaking transition, in which the collapsed state has no preferred in-plane direction because of the axisymmetry of the everted shell. When the axisymmetric everted configuration is stable, a finite perturbation can trigger rapid snap-through toward a lower-energy collapsed equilibrium, accompanied by substantial volume contraction and a triggering response that is relatively insensitive to boundary constraints. We further show that assemblies of these shells behave as granular energy-absorbing systems, exhibiting a stable stress plateau, delayed densification, and substantial frictional dissipation during collective rearrangement. These results provide a mechanics-based route for designing shell assemblies with robust, direction-insensitive energy absorption.
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