Taffetani Matteo, Vella Dominic
Mathematical Institute, University of Oxford, Woodstock Rd, Oxford OX2 6GG, UK
Mathematical Institute, University of Oxford, Woodstock Rd, Oxford OX2 6GG, UK.
Philos Trans A Math Phys Eng Sci. 2017 May 13;375(2093). doi: 10.1098/rsta.2016.0330.
We consider the point indentation of a pressurized elastic shell. It has previously been shown that such a shell is subject to a wrinkling instability as the indentation depth is quasi-statically increased. Here we present detailed analysis of this wrinkling instability using a combination of analytical techniques and finite-element simulations. In particular, we study how the number of wrinkles observed at the onset of instability grows with increasing pressurization. We also study how, for fixed pressurization, the number of wrinkles changes both spatially and with increasing indentation depth beyond onset. This 'Far from threshold' analysis exploits the largeness of the wrinkle wavenumber that is observed at high pressurization and leads to quantitative differences with the standard 'Near threshold' stability analysis.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'
我们考虑一个受压弹性壳的点压痕问题。此前已经表明，随着压痕深度准静态增加，这样的壳体会出现起皱失稳现象。在此，我们结合解析技术和有限元模拟对这种起皱失稳进行详细分析。特别地，我们研究在失稳起始时观察到的皱纹数量如何随增压增加而增长。我们还研究了在固定增压情况下，皱纹数量如何在空间上变化，以及在失稳起始后如何随压痕深度增加而变化。这种“远离阈值”分析利用了在高增压情况下观察到的大皱纹波数，并导致与标准的“接近阈值”稳定性分析存在定量差异。本文是主题为“复杂介质中通过失稳进行图案化：理论与应用”这一特刊的一部分。
