Numerical analysis of wood subjected to bending and northern European climate

Due to the natural process of sorption, wood constantly interacts with the surrounding climate to establish an equilibrium moisture content, even without the direct influence of rain, solar radiation or wind. However, when wood is subjected to a combination of a change in moisture content and a state of stress brought on by e.g. mechanical load, differential shrinkage or swelling, or differences in material properties, a continuous change in the level of stress and the occurrence of deformations and fracture can be the result. The techniques available for in-situ monitoring of changes in moisture content and hygro-mechanical and viscoelastic behaviour can only be employed in specific locations in or around the wood. Whereas, modern techniques employed in laboratories, such as digital image correlation and computed tomography are laborious and time consuming. With recent developments in three-dimensional modelling, endless predictions can be made both of moisture flow and of the hygro-mechanical and visco-elastic behaviour of wood in three-dimensional space, requiring experimental data only to calibrate and validate the model. A three-dimensional numerical model was created in finite element software Abaqus FEA® to simulate both the transient nonlinear moisture flow and the moisture-dependent distortion and stress, while account is being taken of the fibre orientation (annual ring pattern, conical shape and spiral grain). A nonlinear single-Fickian model in connection with a nonlinear Neumann boundary condition is used to describe the moisture flow. For a moisture-sensitive and visco-elastic material such as wood, it is common to describe the total strain rate as a summation of the elastic, hygro-expansion, visco-elastic creep and mechano-sorptive strain rates. The aim was to determine whether the model was able to simulate in an adequate way the beam bending that occurs under northern European climate conditions. To accomplish this, the following steps were taken: 1) on the basis of experimental data available in literature, a set of expressions was created to describe the moisture- and temperature-dependent diffusion coefficient and surface emission coefficient, 2) experimental results obtained for small beams tested under constant temperature and systematic relative humidity (controlled climatic) conditions were used to calibrate the numerical model, account being taken of the spiral grain that applied and the annual ring curvature, and 3) test results for solid beams tested in northern European (natural) climatic conditions were used to validate the numerical model, account being taken of the fibre orientation. The results obtained showed a clear distinction between the effect of moisture on the stress development caused by mechanical load and the stress development caused solely by changes in climate. The changes in moisture that occurred were found to have the strongest effect on the stress state that developed in areas in which the tangential direction of the material was aligned with the exchange surface of the beams. Such areas were found to be exposed to high-tension stress during drying and to a stress overturn brought about by wetting. The material orientation showed to have a strong effect on the estimated deflection, calibrated material parameters and normative stress states