3D multiscale micromechanical model of wood: From annual rings to microfibrils

A 3D micromechanical analytical-computational model of softwood, which takes into account the wood microstructures at four scale levels, from microfibrils to annual rings, is developed. For the analysis of the effect of the annual rings structure on the properties of softwood, an improved rule-of-mixture model, based on 3D orthotropic stress–strain relations and taking into account the compatibility of deformations at the interface of two phases and equilibrium of tractions at phase boundaries, is proposed. The improved rule of mixture model (IRoM) was compared with the classical rule-of-mixture (RoM) and finite element method (FEM) simulations. It was shown that IRoM gives almost as good results as FEM. The analytical model of annual rings is combined with the 3D finite element model of softwood as cellular material with multilayered, microfibril reinforced cell walls, developed by Qing and Mishnaevsky, 2009a, Qing and Mishnaevsky, 2009b. Using the combined four-level model, the effect of wood density, microfibril angle (MFA) and cell shape angle (CSA) on the Young’s moduli, Poisson’s ratios and shrinkage properties of softwood has been investigated in numerical experiments. The simulations were verified by comparison with experimental data.