INRA/UMR 547 PIAF (Physique et physiologie Intégratives de l'Arbre Fruitier et forestier), 234 avenue du Brézet, F-63000 Clermont-Ferrand, France.
J Theor Biol. 2011 Mar 21;273(1):115-29. doi: 10.1016/j.jtbi.2010.12.027. Epub 2010 Dec 25.
Trees are able to maintain or modify the orientation of their axes (trunks or branches) by tropic movements. For axes in which elongation is achieved but cambial growth active, the tropic movements are due to the production of a particular wood, called reaction wood which is prestressed within the growing tree. Several models have been developed to simulate the gravitropic response of axes in trees due to the formation of reaction wood, all within the frame of linear elasticity and considering the wood maturation as instantaneous. The effect viscoelasticity of wood has, to our knowledge, never been considered. The TWIG model presented in this paper aims at simulating the gravitropic movement of a tree axis at the intra-annual scale. In this work we studied both the effect of a non-instantaneous maturation process and of viscoelasticity. For this purpose, we considered the elastic case with maturation considered as an instantaneous process as the reference. The introduction of viscoelasticity in TWIG has been done by coupling TWIG to a model developed for bridges. Indeed from a purely mechanical point of view, bridges and trees are very similar: they are structures which are built in stages, they are made of several materials (composite structures), their materials are prestressed (wood is prestressed during the maturation process as a result of polymerisation of lignin and cellulose to form the secondary cell wall and concrete is prestressed during drying). Simulations gave evidence that the reorientation process of axes can be significantly influenced by the kinetics of maturation. Moreover the model has now to be tested with more experimental data of wood viscoelasticity but it appears that in the range of a relaxation time from 0 to 50 days, viscoelasticity has an important effect on the evolution of tree shape as well as on the values of prestresses.
树木能够通过向性运动来维持或改变其轴（树干或树枝）的方向。对于那些伸长已完成但形成层仍活跃的轴，向性运动是由于产生了一种特殊的木材，称为反应木，它在生长中的树木内受到预应力。已经开发了几种模型来模拟由于反应木的形成而导致的树木轴的向重力反应，所有这些模型都在线性弹性的框架内，并考虑木材的成熟是瞬时的。据我们所知，木材的粘弹性的影响从未被考虑过。本文提出的 TWIG 模型旨在模拟树木轴的年际范围内的向重力运动。在这项工作中，我们研究了非瞬时成熟过程和粘弹性的影响。为此，我们考虑了将成熟视为瞬时过程的弹性情况作为参考。在 TWIG 中引入粘弹性是通过将 TWIG 与为桥梁开发的模型耦合来实现的。事实上，从纯粹的力学角度来看，桥梁和树木非常相似：它们是分阶段建造的结构，由多种材料（复合材料结构）组成，它们的材料受到预应力的作用（木材在成熟过程中受到预应力的作用，这是由于木质素和纤维素聚合形成次生细胞壁，以及在干燥过程中混凝土受到预应力的作用）。模拟结果表明，轴的重新定向过程可以受到成熟动力学的显著影响。此外，该模型现在必须用更多的木材粘弹性实验数据进行测试，但似乎在松弛时间从 0 到 50 天的范围内，粘弹性对树木形状的演变以及预应力值有重要影响。
