Numerical modelling of shape regulation and growth stresses in trees

The main objective of this paper is to present the results of a study of the interactions between the growth and design of a tree with regards to biomechanical factors at the plant level. A numerical incremental model dedicated to the calculation of tree mechanical behaviour has been integrated in the plant architecture simulation software AMAPpara. At any stage of tree growth, a new equilibrium was calculated considering the weight increment applied on the structure, i.e. the mass of new wood layers and vegetative elements, as well as the biomechanical reaction caused by cell maturation strains in both normal and reaction wood. The resulting incremental displacements allowed the tree shape to be modified. The field of growth stresses was calculated within the stem, using a cumulative process taking into consideration the past history of each growth ring. The simulation results of trunk and branch shape, as well as internal stresses, were examined after consideration of different growth strategies. A block of trees was also simulated in order to show the influence of spatial competition on stem curvature and the variability in growth stress.