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Morphogénèse et élasticité en géométrie mince

Abstract : Biological soft tissues develop mechanical stresses when they grow. In close association with biological factors, those stresses contribute to shape living objects. In this work, we have explored the coupling between growth and elasticity, with a strong focus on thin bodies, either free or confined in space. We first derive a theory describing the deformations of a thin plate subjected to an arbitrary growth field. In this geometrical limit, the growth process has a simple and elegant interpretation : it is a source of mean and Gaussian curvatures. As an illustration of the theory, we study two example drawned from plant development and we show how the inhomogeneity and anisotropy of the growth field may result in spontaneous deformations. In a second time we study a generic case of confined growth in which a thin sample is bounded on one side to an elastic substrate. The accessible deformations are drastically reduced and we investigate this physical situation in a mechanical model of melanoma development. In particular, we show that this confinement, frequently encoutered in animal tissues, can lead to a stress focusing during growth. Using swelling hydrogels, we then realise an artificial tumor in which growth is confined at the periphery . The experimental results are coherent with observations on melanoma although important distinctions between biological growth and swelling are highlighted. We then discuss the inhibition of growth by mechanical stresses and precise the role of hydrogels as substitutes for biological tissues.
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https://tel.archives-ouvertes.fr/tel-00544143
Contributor : Julien Dervaux <>
Submitted on : Tuesday, December 7, 2010 - 1:39:06 PM
Last modification on : Wednesday, December 16, 2020 - 9:28:01 AM
Long-term archiving on: : Tuesday, March 8, 2011 - 4:17:34 AM

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  • HAL Id : tel-00544143, version 1

Citation

Julien Dervaux. Morphogénèse et élasticité en géométrie mince. Biophysique [physics.bio-ph]. Université Paris-Diderot - Paris VII, 2010. Français. ⟨tel-00544143⟩

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