Longitudinal growth stresses in trees: analytical models and functional implications
Résumé
During growth, trees develop mechanical stresses of high magnitude having a par cular distribu on across the sec ons of stems and branches. These growth stresses result from the cumulated effect of the loading associated to the increasing weight and the genera on of matura on stress at the tree periphery. Interest on this ques on is mo vated by both its technological implica ons (deforma on and cracks in sawn products) and the comprehension of its biomechanical func on in the living tree. In this presenta on, new analy cal developments and their func onal implica ons will be presented. As an extension of the well-known Kübler's model, simple analy cal models were developed to calculate the field on longitudinal growth stresses in stems. Different canonical cases are considered: (i) a straight axisymmetric trunk, (ii) a branch that bends without reac ng, and (iii) a sta onary lted stem (i.e. a stem keeping its shape constant during growth). The stress field resul ng from growth in these cases will be shown, using realis c parameters taken from various literature sources. These parameters define how the stem size, weight and matura on stress change during tree growth. In order to validate these models, simulated stress fields will be compared to measured pa+erns of residual strains. Finally, the results will be discussed with respect to their func onal implica ons. Three func ons of growth stresses can be dis nguished: the "motor" func on enabling stem to re-orient in response to disturbance, the "posture control" func on enabling stems to keep a constant shape during growth by counterac ng the effect of gravity, and the "skeletal" func on related to the consequences of pre-stressing in terms of resistance to external bending loads. The conclusion enhances the fact that growth stresses in sta onary lted stems (e.g. a branch or tree at a forest border) are asymmetric, and that this asymmetry is adapted to op mize the resistance against wind loading.