Multi-scale analysis of the hygro-mechanical behaviour of oak wood:A numerical and experimental study

Wood has been a fundamental material throughout history, serving structural and decorative purposes, with its enduring significance reflected, amongst other, in wooden cultural heritage (WCH) that reflects the historical, cultural, and artistic values of human civilization. Its unique mechanical properties, combined with its aesthetic and renewable qualities, underscore its importance as a sustainable and environmentally friendly material. However, the inherent complexities of wood, including its sensitivity to environmental factors, such as humidity and the aging processes of its polymers - lignin, cellulose and various hemicelluloses - pose significant challenges that necessitate a deep understanding of its behavior across multiple scales. The preservation of wooden cultural heritage and art objects in museums highlights the critical need for such understanding. These artifacts, often centuries old, have been subjected to fluctuating environmental conditions that exacerbate degradation. Humidity changes can induce irreversible deformations, cracking, and a reduction in stiffness and strength due to the aging of wood’s chemical and physical structures. Effective conservation of these culturally significant objects demands an advanced approach that bridges the gap between the ultra-structural characteristics of wood and its macroscopic behavior. This thesis tackles these challenges by introducing a comprehensive multi-scale framework to predict the hygro-mechanical response of oak wood, a material extensively used in cultural heritage objects. The presented framework uniquely integrates four distinct scales of observation, i.e., the nano-, micro-, meso-, and macro-scales, enabling the incorporation of structural and physical effects from each scale into the effective macroscopic behavior. At the nano-scale, the model captures the moisture-dependent behavior of cellulose microfibrils within a hemicellulose and lignin matrix, which forms the basis for modelling and understanding the response at higher scales. At the micro-scale, the model accounts for the layered structure of wood cell walls, while at the meso-scale it considers the cellular structure of growth rings with variable densities. These features are linked across the various length scales using asymptotic homogenization or Voigt averaging techniques, to finally obtain the effective hygro-elastic properties at the macro-scale. An essential component of the framework is the application of a three-dimensional level set-based image segmentation method, which has been developed to identify and characterize complex oak wood micro-structures. This method, which is based on the Local Chan-Vese energy functional, accurately distinguishes cell wall material from void spaces, and further segments the cellular material into axial cells and ray parenchyma cells. High-resolution micro-structural images obtained through X-ray micro-computed tomography (μCT) enable the extraction of statistical data on cell dimensions and wall thicknesses. The robustness and accuracy of the segmentation method allow for a detailed morphological analysis of oak micro-structures, providing essential input for finite element models. Based upon the segmented meso-structures, the multi-scale computational model predicts the macroscopic hygro-mechanical response of oak wood. Utilizing detailed three-dimensional representations of oak growth rings, the model applies the extended finite element method (XFEM) for the discretization of the material structure at the meso-scale, and combines this with asymptotic homogenization to obtain the effective hygro-mechanical properties at the macro-scale. Computational results demonstrate the model’s ability to realistically simulate moisture-dependent behavior and identify critical stress sites where damage may occur under fluctuations in relative humidity. The predicted macro-scale properties agree well with experimental data, thereby demonstrating the accuracy and practical applicability of the modelling framework. The integration of experimental and computational methods, as presented in this thesis, provides a powerful toolset for understanding and predicting the complex hygro-mechanical behavior of oak wood. The multi-scale approach not only advances the scientific understanding of wood’s structural responses at various scales of observation, but also offers practical solutions for the conservation of wooden cultural heritage, ensuring its sustainability and integrity for future generations.