Selected Constitutive Models for Simulating the Hygromechanical Response of Wood

The present thesis is a compilation of papers. Three of the papers, I , VI and VII, are published in this thesis only, i.e., an introductory paper and two so-called discussion papers. The papers II, III and V have been published in the international journal, Holzforschung. Paper IV is a conference paper presented at the 19^th Nordic Seminar on Computational Mechanics, Lund, Sweden, 2006.

Paper I: The theories for the phenomena leading to hygromechanical response of wood relate to the orthotropic cellular structure and the hydrophilic and hydrophobic polymers constituting the cells. This introductory paper presents these theories for the hygromechanical response and hereby also provides the frame of reference and the connecting thread of the present thesis.

Paper II: Multiple paths for moisture transport and slow sorption yield non-Fickian effects. This calls for a new type of multi-phase transport model. In this paper a so-called multi-Fickian model is revised with respect to the incorporated essential sorption rate model. Based on existing experimental results the sorption rate model is studied. A desorption rate model analogous to the adsorption rate model is proposed. Furthermore, the boundary conditions are discussed based on discrepancies found for similar research on moisture transport in paper stacks.

Paper III: A new sorption hysteresis model suitable for implementation into a numerical method is developed. The prevailing so-called scanning curves are modeled by closed-form expressions, which only depend on the current relative humidity of the air and current moisture content of the wood. Furthermore, the expressions for the scanning curves are formulated independent of the temperature and species-dependent boundary curves.

Paper IV: The sorption hysteresis model developed in paper III is applied to two different wood species and to bleach-kraft paperboard.

Paper V: The sorption hysteresis model is implemented into the multi-Fickian model allowing simultaneous simulation of non-Fickian effects and hysteresis. A key point for this implementation is definition of the condition of wood as a state in the sorption hysteresis space, which is independent of the condition of water vapor in the lumens. Two approaches are developed and tested by implementation into commercial software.

Paper VI: The temperature dependencies of the hysteretic multi-Fickian moisture transport model are discussed. The constitutive moisture transport models are coupled with a heat transport model yielding terms that describe the so-called Dufour and Sorret effects, however, with multiple phases and hysteresis included.

Paper VII: In this paper the modeling of transverse couplings in creep of wood are discussed based on experimental observation of time dependent Poisson ratios and new theoretical findings on the Poisson ratio. A new orthotropic creep model, which provides directionally independent creep rates, is proposed. Furthermore, the procedure for an ongoing experimental study of the phenomenon is presented.