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Tip growth in morpho-elasticity

Abstract : Growth of living species generates stresses which ultimately design their shapes. As a consequence, complex shapes, that everybody can observe, remain difficult 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 leaves in the spring. However, even in this case the diversity of shapes is really vast. Here, we focus on growing 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 affect its final shape. Two models of finite elasticity are considered: the Neo-Hookean and the poro-elastic model with incompressibility.
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Submitted on : Wednesday, December 9, 2020 - 9:54:05 AM
Last modification on : Friday, December 3, 2021 - 11:43:50 AM
Long-term archiving on: : Wednesday, March 10, 2021 - 6:35:22 PM

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Martine Ben Amar, Julien Dervaux. Tip growth in morpho-elasticity. Comptes Rendus Mécanique, Elsevier, 2020, 348 (6-7), pp.613-625. ⟨10.5802/crmeca.27>⟩. ⟨hal-03047964⟩

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