The mechanical design of trees and wood is suited to face two types of mechanical loads: permanent loads related to the increase in self-weight, and temporary loads due to external actions such as wind. In angiosperms, a tensile longitudinal stress is always generated around the tree periphery during wood formation. This maturation stress plays a key role in terms of biomechanical adaptation of the tree to its environment: it provides the stem with a motor system allowing the postural control of the tree (i.e. compensating for the effect of permanent loads) and, eventually, the reorientation of stems and branches in response to disturbance. Another important function of this tensile pre-stress located at the periphery is to improve the bending resistance of stems against temporary loads, by compensating for the relatively low compressive strength of green wood. As consequence of maturation stress production, compressive growth stress accumulates in the core of the trunk. A numerical model was formulated and implemented to compute the field of longitudinal growth stress across a growing cross-section, and to calculate ecologically relevant parameters defined as the "performance of the motor system" and the "safety against temporary bending". The model is general enough to account for any cross-section shape, growth eccentricity, viscoelastic behavior of wood and heterogeneity of wood mechanical properties (stiffness and maturation stress). Simulations were performed to evaluate the influence of these parameters on the growth stress pattern, motor performance, and safety against temporary bending. Results show that in some situations, the growth stress pattern can have a negative impact on the bending safety. A sensitivity analysis was performed and evidences that, in some case, the motor performance can be only improved at the expense of a lower safety against bending loads. Conclusions emphasize the fact that the value of biomechanical parameters mediates a trade-off between the motor performance of the stem and its safety against temporary loads, and that the range of real value of biomechanical parameters is close to optimal regarding this trade-off.
The bending mechanics of tree stems: the key role of wood maturation stress for resisting both permanent and temporary loads