Tension-dependent transverse buckles and wrinkles in twisted elastic sheets
Tension-dependent transverse buckles and wrinkles in twisted elastic sheets
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DOI：
10.1098/rspa.2018.0062
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发表时间：
2018-06-01
影响因子：
3.5
通讯作者：
Chopin, J.
中科院分区：
文献类型：
--
作者：
Kudrolli, A.;Chopin, J.
本文用实验方法研究了长L、宽W、厚t的弹性薄板在张力T作用下两端夹紧的扭转诱导横向屈曲不稳定性。在临界张力T-λ和临界扭转角eta（tr）以上，我们发现，在扭转轴的横向上，板的振型数n >= 1。通过引入可弯曲长度LB和夹持长度L-C（< L-B），确定了夹持主导、可弯曲和刚性三种不同的屈曲状态。在刚性区域（L > L-B），我们发现n = 1的模式在eta（tr）= eta（S）以上发展，类似于（t/W）T-1/2，与L无关。在可弯曲状态L-C < L< L-B中，n = 1以及n > 1出现在eta（tr）= eta（B）之上，类似于根t/LT-1/4。这里，我们发现当n > 1时，波长λ（B）类似于根LtT（-1/4）。这些缩放同意从协变形式的Foppl-von Karman方程，然而，我们发现，n = 1模式也在一个令人惊讶的大范围的L在可弯曲的制度。最后，在夹紧控制区域（L < L-C），我们发现由于夹紧边界条件引起的附加刚度，eta（tr）比eta（B）高。
We investigate with experiments the twist-induced transverse buckling instabilities of an elastic sheet of length L, width W and thickness t, that is clamped at two opposite ends while held under a tension T. Above a critical tension T-lambda and critical twist angle eta(tr), we find that the sheet buckles with a mode number n >= 1 transverse to the axis of twist. Three distinct buckling regimes characterized as clamp-dominated, bendable and stiff are identified, by introducing a bendability length LB and a clamp length L-C(< L-B). In the stiff regime (L > L-B), we find that mode n = 1 develops above eta(tr) = eta(S) similar to (t/W)T-1/2, independent of L. In the bendable regime L-C < L< L-B, n = 1 as well as n > 1 occur above eta(tr) = eta(B) similar to root t/LT-1/4. Here, we find the wavelength lambda(B) similar to root LtT(-1/4), when n > I. These scalings agree with those derived from a covariant form of the Foppl-von Karman equations, however, we find that the n = 1 mode also Occurs over a surprisingly large range of L in the bendable regime. Finally, in the clamp-dominated regime (L < L-C), we find that eta(tr) is higher compared to eta(B) due to additional stiffening induced by the clamped boundary conditions.