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A model to simulate the gravitropic response and internal stresses in trees, considering the progressive maturation of wood

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Abstract

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The developed model of gravitropism takes non-instantaneous maturation of wood into account which enabled to correctly simulate different gravitropic phases and realistic internal stress profiles.

Abstract

A new biomechanical model of tree movement in relation to gravity (gravitropism) is proposed in this study. The modelling of the progressive maturation of wood cells is taken into account, as well as spatio-temporal variations in maturation strains (MS) and mechanical properties. MS were identified using an inverse method that allows the model to fit the gravitropic reaction observed experimentally. For this purpose, the curvature during righting movement, the geometry and the mass distribution of a two-year-old poplar tree was measured. The identified MS are higher than expected, which shows the underestimation of MS by usual measurements. By using the same mechanical parameters and MS as an input, the model gives satisfying results in terms of shape modelling for different trees up to 32 days after tree tilting. The model is able to simulate the latency phase observed in the tree righting movement, and the internal stress profile in the trunk is realistic (low compressive value in the central part of the trunk and zero stress in newly formed cells). The next development of the model will aim to simulate the end of the gravitropic phase in relation with the regulation of MS by the tree.

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Conflict of interest

The authors declare that they have no conflict of interest.

Author information

Authors and Affiliations

  1. LaBoMaP, Arts et Metiers ParisTech, Rue Porte de Paris, 71250, Cluny, France

    Guillaume Pot

  2. INRA, UMR 547 PIAF, 63100, Clermont-Ferrand, France

    Catherine Coutand & Marc Saudreau

  3. Clermont Université, Université Blaise Pascal, UMR 547 PIAF, 63000, Clermont-Ferrand, France

    Catherine Coutand & Marc Saudreau

  4. UMR 6602, Institut Pascal, CNRS, 63171, Aubière, France

    Evelyne Toussaint

  5. Clermont Université, Université Blaise Pascal, Institut Pascal, BP 10448, 63000, Clermont-Ferrand, France

    Evelyne Toussaint

  6. Institut de Physique de Rennes, UMR 6251, Universite de Rennes 1, Campus de Beaulieu, 35042, Rennes, France

    Jean-Benoît Le Cam

Authors
  1. Guillaume Pot
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  2. Catherine Coutand
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  3. Evelyne Toussaint
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  4. Jean-Benoît Le Cam
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  5. Marc Saudreau
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Corresponding author

Correspondence to Guillaume Pot.

Additional information

Communicated by R. Hampp.

This work was supported by a grant from the Auvergne Regional Council and the European Regional Development Fund.

Authors contributions to the paper:

G. Pot participated to model building, simulations analyses and writing of the paper.

C. Coutand participated to model building, simulations analyses and writing of the paper.

E. Toussaint participated to model building, simulations analyses and writing of the paper.

J. B. Le Cam participated to model building, simulations analyses and writing of the paper.

M. Saudreau participated to the optimization procedure for the identification of the parameters of the model.

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Pot, G., Coutand, C., Toussaint, E. et al. A model to simulate the gravitropic response and internal stresses in trees, considering the progressive maturation of wood. Trees 28, 1235–1248 (2014). https://doi.org/10.1007/s00468-014-1033-y

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  • DOI: https://doi.org/10.1007/s00468-014-1033-y

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