# Modelling of dynamic and quasistatic events with special focus on wood-drying distortions

Abstract: This thesis deals mainly with computer simulations of wood-drying distortions, especially twist. The reason for this is that such distortions often appear in dried timber, and the results are quality downgrades and thus value losses in the wood value chain. A computer simulation is a way to theoretically simulate what happens in reality when moisture content in timber changes. If the computer simulation model is appropriate and capable of realistic simulations of real events, then it is possible to study what happens with the timber distortions if some parameters in the simulation model are changed. In that way, a good simulation model is a good tool to use when trying to reduce wood-drying distortions by altering some parameters in the process of producing timber. Computer simulations have the comparative advantage over real-world experiments of being cheaper and faster to perform, but the disadvantage that the outcome may be doubtful if the simulation model is bad. Wood is an anisotropic material that is often modelled as an orthotropic material, i.e., a material that has three orthogonal directions at each point with different material properties. A method to measure the orthotropic directions in wood nondestructively was the subject of paper 1. The method was to calculate the directions from the information in a series of two-dimensional computed tomography (CT) images. Fictitious, small calculation spheres were distributed in the wood material, and the principal directions of inertia of these spheres were calculated using the density information in the CT images. The principal directions were assumed to be the radial, the tangential and the fibre direction at the point in question. Tests of the method on three wood samples showed that the method works, but that there was considerable spread in the results from individual spheres. The spread was reduced by calculating mean values for a number of spheres in the vicinity of each other. Twist of timber depends on various influencing variables. Traditionally, a formula from the late 50s by Stevens and Johnston, valid for single growth ring cylinders, has often been used to explain which variables influence twist. One interesting influencing variable in this formula is the spiral grain angle; the others are the moisture content change, the coefficient of moisture expansion and the radius of the growth ring cylinder in question. However, real boards are not single growth ring cylinders, and paper 2 deals with the dependence of twist of realistic boards on various influencing variables. Derivations were made on a theoretical and analytical level of the twist of timber, and the result was a formula whose first term corresponds to Stevens and Johnston's original formula; but the formula has also a second term. This second term is proportional to the gradient of the spiral grain angle and is especially important for timber sawn far from pith. The validity of the second term was shown by comparisons with finite element method (FEM) results and also with experimental results. The first step in simulating wood-drying distortions is to simulate the wood-drying process. The output of this moisture transport simulation is the moisture content of the wood piece as a function of time. We then use this output as input to a second step in which we simulate the shrinkage and deformation of the wood piece. A diffusion model was used here to simulate moisture transport, and this simulation requires diffusion and mass transfer coefficients. Such values from drying Norway spruce (Picea abies) sapwood were measured and reported in paper 3. Measurements of the moisture content during drying of a sample were made with CT, and the diffusion coefficient was evaluated with two methods. The first method used a one-dimensional and the second a two-dimensional diffusion model. No assumptions of the dependence of the diffusion coefficient on any functions or variables were made beforehand. Both methods showed about the same result and dependence on moisture content, but also on depth (distance from surface) of the diffusion coefficient. The depth dependence was only apparent near the surface. Comparisons of the evaluated values of the diffusion coefficient in general terms with other results were made and showed agreement. Industrial process changes aimed at reducing twist distortions are interesting to study. In paper 4, simulations of drying distortions were conducted, and pretwist during drying as a remedy to overcome twist of boards was tried. Paper 4 also contained results from laboratory experiments on the influence of the spiral grain angle and the degree of restraint and pretwist during drying on twist of boards. Results from an industrial test of the influence of the spiral grain angle and the degree of restraint on twist of boards were also described. The laboratory experiments and the industrial test were simulated with an FEM simulation model in two stages. First, the FEM model was calibrated by adjusting the yield stresses of the wood material in order for the results from the laboratory experiments to agree with the simulation model results. Then in a second stage, the simulation model was used to simulate the industrial test. The results showed that the FEM simulation model was capable of producing realistic results, but that there were some discrepancies between the industrial test results and the simulation results. The discrepancies were assumed to be due to biased measurements, insufficient knowledge of the distribution of the spiral grain angle or other causes.

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