TWIG: a model to simulate the gravitropic response of a tree axis in the frame of elasticity and viscoelasticity, at intra-annual time scale

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.