MECHANICS OF STANDING TREES - MODELING A GROWING STRUCTURE SUBMITTED TO CONTINUOUS AND FLUCTUATING LOADS .2. TRIDIMENSIONAL ANALYSIS OF MATURATION STRESSES - CASE OF STANDARD HARDWOOD

A model of tridimensional mechanical stresses due to wood differentiation is derived from the previously presented theoretical analysis (see Part 1) of mechanical stresses which develop in stems as the tree grows. The model is based on a simple rheological scheme for cellular maturation: wood is supposed to have a tendency to strain during the formation of the secondary cell wall. In normal wood, this tendency takes the form of a longitudinal shrinkage and a transverse swelling, that agrees with micro-mechanical modelling of lignification and crystallizing of cellulose in the S2 layer. In the living tree, this trend is impeded by the mass of the whole trunk, so wood is submitted to internal stresses, namely maturation stresses. This model generalizes former theories on growth stress patterns in tree stems, and the parameters of the model (the elastic compliances of green wood, the tree diameter, the residual strains at the standing stem surface) are still evaluated by current experiments. Stresses patterns are then computed in a standard situation, which uses realistic averaged values of parameters for a hardwood cross-section, composed of radially homogeneous wood, but which shows the circumferential asymmetry of residual strains usually observed. These patterns commonly show longitudinal tensile stresses and tangential compressive ones in the outer part of the trunk, equilibrated by longitudinal compressive stresses and transverse tensile ones in the inner part of the trunk. The angular asymmetry induces, on the one hand, higher values of these components and their radial variations on one side of the tree; on the other hand, transverse shear stresses. These maturation stresses are finally superimposed to support stresses due to tree self-weight - the addition of support stresses and maturation stresses are called "growth stresses", and to felling stresses due to the removal of this self-weight, analysed in former papers (see Part 1). As analysed in Part 1, support stresses are not the opposite of felling stresses but depend on the entire history of the tree; so it is quite difficult to separate the effects of support and maturation when experimental results on internal stresses in living trees or logs are observed. Nevertheless, the conclusion is that in general, maturation stres distributions determine the patterns and the magnitude of growth stresses in a living tree or a log, although particular problems may require careful consideration: for instance, in the standard situation of a highly disymmetric leaning reorienting tree, the longitudinal growth stress gradient near the surface (which is responsible for the deflections of planks) is lower than the longitudinal maturation stress gradient.