Tip growth in morpho-elasticity
Tip growth in morpho-elasticity
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DOI：
10.5802/crmeca.27
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发表时间：
2020-11
期刊：
影响因子：
--
通讯作者：
M. B. Amar;J. Dervaux
中科院分区：
文献类型：
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作者：
M. B. Amar;J. Dervaux
.生物物种的生长产生的压力最终决定了它们的形状。阿萨的结果是，每个人都能观察到的复杂形状仍然难以预测，即使生长生物学过于简单化，艾德也是如此。解决这个问题的一种方法是将我们自己限制在准平面的物体上，比如弹簧中的树枝状突起。然而，即使在这种情况下，形状的多样性也是非常巨大的。在这里，我们将重点放在生长尖端上，目的是将它们在弹性生长中的作用与经典的粘性鳍状突起和树枝状突起进行比较。借助于复变函数的分析，我们证明了一个抛物线在增长过程中是无应力的，但任何增长扰动都将强烈地改变它的最终形状。考虑了两种有限弹性模型：新胡克模型和不可压缩的孔隙弹性模型。简历
. Growthofliving species generates stresses whichultimately design their shapes. Asa consequence, complex shapes, that everybody can observe, remain di ffi cult to predict, even when the growth biology is over-simplified. One way to tackle this question consists in limiting ourselves to quasi-planar objects like leavesinthespring.However,eveninthiscasethediversityofshapesisreallyvast.Here,wefocusongrowing tips with the aim to compare their role in elastic growth to classical viscous fingering and dendritic growth. With the help of complex analysis, we show that a parabola under constant growth is free of stress while growing but any growth perturbation will strongly a ff ect its final shape. Two models of finite elasticity are considered: the Neo-Hookean and the poro-elastic model with incompressibility. Résumé