Effects of cellulose fibril cross-linking on the mechanical behavior of wood at different scales

Predicting the influence of structural parameters on wood elasticity is useful for engineering application, however due to the complex imbrication of several scales it is important to know which features need to be taken into account. The aim of this work is to investigate the influence on wood stiffness of waviness and interconnection of cellulosic fibrils, an observed feature usually overlooked in micromechanical models. For that, a multi-scale model estimating the macroscopic behavior of wood is developed. This model integrates three different scales of wood structure: that of the cell wall, that of the cellular tissue and that of the growth ring. It relies on both numerical and analytical homogenization procedures to determine their effective behavior by defining at each scale a periodic representative volume element. Using this multi-scale model, it is shown that the influence of the oscillations and interconnections of the fibrils is significant for certain moduli at the macroscopic level (ring scale), such as the macroscopic shear moduli, while it can be neglected for others. Furthermore, although the effect of fibril crosslinks is quite strong for certain components of elastic behavior at the cell wall level, it loses its importance at the macroscopic level, especially for low-density wood. This trend can be explained by the anti-symmetric tilt of fibrils in adjacent cell walls. On the other hand, for denser woods where the interactions between adjacent cell walls are less dominant, or in the case of softened wood, the effect of fibril oscillations remains important.