Multiphase continuum modeling of wood: A hybrid mixture theory approach

Abstract

Wood has been used as a construction material for a very long time. The development of efficient industrial production processes of wood has expanded the use of the material with the introduction of new products, such as engineered wood products. Considering the adversely changing climate, the use of wood in construction is advocated due to its environmental benefits, such as its low carbon footprint. As a naturally growing material, however, wood has a high moisture content when harvested. Additionally, the chemical composition of wood fibers together with its porous structure, gives wood a strong affinity towards moisture, throughout the whole lifecycle of the material. The moisture content in wood strongly influences its physical and mechanical properties, such as strength, stiffness, shape stability and durability properties. Further, it requires energy-intensive drying processes to bring wood to the desired moisture content for structural use. The task of predicting the moisture content and transport of moisture in wood is challenging. It involves multiple phases, i.e., liquid water, gaseous vapor and the solid wood fibers, and it also engages a number of physical processes such as evaporation/condensation, adsorption/desorption, diffusion and seepage of the fluids, heat conduction and swelling/shrinkage of the wood fibers. This thesis investigates the interplay between heat, moisture and their associated transport mechanisms in wood. The mechanics of the solid wood material is also studied. The primary goal of this thesis is to develop a thermodynamically consistent continuum model that is capable of predicting the macroscopic behavior of wood subjected to varying climate conditions and mechanical loading. The hybrid mixture theory is used todevelop a multiphase continuum model for wood, in which, at the macroscale, the wood material is considered to contain immiscible solid, liquid and gaseous phases. Constitutive relations are derived by fulfillment of the entropy inequality at the macroscopic scale. Interaction processes involving phase changes through sorption and evaporation/condensation, and diffusive transport mechanisms are described using the macroscale chemical potential as defined by the hybrid mixture theory. The thesis starts with introductory chapters describing the overall properties of wood of importance in this context and the interactions between wood and moisture. A summary of the mixture theory as applied to this work is also presented. The thesis contains four attached papers, Paper I, Paper II, Paper III and Paper IV. In Paper I a model describing moisture transport and sorption processes in wood below the saturation point of the wood fibers is presented. The model is developed further, in Paper II and Paper III, to incorporate wood-water interactions below and above the fiber saturation point. Shrinkage/swelling and non-linear elastic deformations are also implemented. A drying test simulation of wood starting from the green state is performed and compared to experimental results. The model presented in Paper II and Paper III is complemented in Paper IV by considering damage associated with anisotropic cracking of the solid wood material. The phase field fracture modeling approach is used for this purpose. The resulting non-linear coupled partial differential equations governing the macroscopic behavior of the material are solved numerically using the finite element method. Simulations are performed to check the overall performance of the theoretical framework behind the proposed models and they are compared to experimental results for the identification of some of the material parameters of the models.