A computational multi-scale model is presented to predict the macroscopic hygro-mechanical behaviour of oak wood, based on detailed three-dimensional mesoscopic representations of entire oak growth rings obtained by X-ray micro-computed tomography ( \(\mu \) CT). The 3D meso-structural volumes acquired by \(\mu \) CT scanning consist of arrays of voxels, with the grayscale intensity values of the voxels denoting the local material densities. A level set-based image segmentation method is applied to distinguish the individual meso-structural phases, including the cell walls and voids (lumen and vessels). A dedicated algorithm based on the spatial gradient of the level set function accurately identifies the local material directions in the cell walls. The individual phases in the meso-scale cellular structure are discretized using the extended finite element method. Here, a moment fitting scheme is applied for an efficient numerical integration in the elements intersected by cell wall boundaries. Finally, asymptotic homogenization is used for computing the effective macro-scale response of oak wood from the hygro-mechanical response of the underlying meso-structure. The macro-scale hygro-mechanical behaviour calculated by the multi-scale model for oak growth rings agrees well with experimental values from the literature. Further, the meso-scale response computed for oak growth rings subjected to a representative moisture content variation allows to identify local, critical sites in which mesoscopic hygro-mechanical damage may occur. The effective hygro-mechanical properties calculated by the multi-scale model may serve as an input for predicting the moisture-dependent mechanical response of oak wood structures and objects subjected to arbitrary hygro-mechanical loading paths.
