Curvature-Driven Wrinkling of Thin Elastic Shells
Curvature-Driven Wrinkling of Thin Elastic Shells
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DOI：
10.1007/s00205-020-01566-8
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发表时间：
2019-06
影响因子：
2.5
通讯作者：
Ian Tobasco
中科院分区：
文献类型：
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作者：
Ian Tobasco
把一个弹性薄壳压平需要多少能量？受最近浮壳起皱规律实验的启发，我们发展了一种严格的方法，通过收敛来回答这个问题，使之在壳体厚度和其他小参数中达到领先的顺序。观察到的图案包括定义良好的皱纹的“有序”区域，以及局部特征不那么健壮的“无序”区域；由于很少或没有施加张力，对有序的偏好并不是最优先的。通过对典型模式能量的重新标度，我们得到了壳体有效位移的极限变分问题。它要求以线性化的方式，用到平面的缩短长度的地图来覆盖最大的区域。凸分析产生了一个边值问题，通过它们的缺陷度量来表征伴随的模式。部分唯一性和正则性定理是由壳的有序部分的特征线法得到的。这样，我们就可以从最小能量原理推导出冲压弹性壳的主阶特征。
How much energy does it take to stamp a thin elastic shell flat? Motivated by recent experiments on the wrinkling patterns of floating shells, we develop a rigorous method via-convergence for answering this question to leading order in the shell’s thickness and other small parameters. The observed patterns involve “ordered” regions of well-defined wrinkles alongside “disordered” regions whose local features are less robust; as little to no tension is applied, the preference for order is nota prioriclear. Rescaling by the energy of a typical pattern, we derive a limiting variational problem for the effective displacement of the shell. It asks, in a linearized way, to cover up a maximum area with a length-shortening map to the plane. Convex analysis yields a boundary value problem characterizing the accompanying patterns via their defect measures. Partial uniqueness and regularity theorems follow from the method of characteristics on the ordered part of the shell. In this way, we can deduce from the principle of minimum energy the leading order features of stamped elastic shells.