The shape of a long leaf
The shape of a long leaf
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DOI：
10.1073/pnas.0911954106
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发表时间：
2009-12-29
影响因子：
11.1
通讯作者：
Mahadevan, L.
中科院分区：
文献类型：
--
作者：
Liang, Haiyi;Mahadevan, L.
陆生植物的长叶和它们在海底的同类——海藻的叶片，具有典型的鞍状中表面和波纹状边缘。为了理解这些形态的起源，我们解剖了叶子和差异拉伸泡沫带，以表明这些形状是由一个简单的原因产生的，即通过弯曲产生的弹性松弛，这种弹性松弛是在叶子的差异生长或超过屈服点的差异拉伸（在带状中）之后产生的。我们量化这些不同的模式，在一个数学模型的形状，最初的平面弹性片与横向梯度纵向增长。通过结合尺度概念、稳定性分析和数值模拟，我们绘制了这些生长带的形状空间，并发现随着相对生长应变的增加，长平坦的薄片变形为马鞍形状和/或产生波动，当生长应变定位于叶片边缘时，波动可能导致强烈的局部波纹。我们的理论描述了几何和生长控制参数，这些参数决定了有限层的形状空间，从而允许对细长叶形态进行比较研究。
Long leaves in terrestrial plants and their submarine counterparts, algal blades, have a typical, saddle-like midsurface and rippled edges. To understand the origin of these morphologies, we dissect leaves and differentially stretch foam ribbons to show that these shapes arise from a simple cause, the elastic relaxation via bending that follows either differential growth (in leaves) or differential stretching past the yield point (in ribbons). We quantify these different modalities in terms of a mathematical model for the shape of an initially flat elastic sheet with lateral gradients in longitudinal growth. By using a combination of scaling concepts, stability analysis, and numerical simulations, we map out the shape space for these growing ribbons and find that as the relative growth strain is increased, a long flat lamina deforms to a saddle shape and/or develops undulations that may lead to strongly localized ripples as the growth strain is localized to the edge of the leaf. Our theory delineates the geometric and growth control parameters that determine the shape space of finite laminae and thus allows for a comparative study of elongated leaf morphology.