Modelling of Dynamic and Quasistatic Events with Special Focus on Wood-Drying Distortions

Mats Ekevad Modelling of dynamic and quasistatic events with special focus on wood-drying distortions Cover: colourful picture made on the computer by Mats Ekevad, “Flying board” Mats Ekevad Modelling of dynamic and quasistatic events with special focus on wood-drying distortions 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 i

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

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.Godkänd; 2006; 20061206 (pafi

Modelling thermoelasticity and hygroelasticity for orthotropic materials

Godkänd; 2009; 20090602 (matse

Three-dimensional orthotropic elastic-plastic-mechano-sorptive material model for simulation of wood behaviour

Godkänd; 2010; 20100831 (matse

Variation of modulus of elasticity in the tangential direction with moisture content and temperature for Norway Spruce (Picea abies)

Modulus of elasticity (MOE) in the tangential direction for Norway spruce, Picea abies (L.) H.Karst was measured. Test samples were tested in three-point bending, and moisture content (MC) and temperature were varied between the green condition and 7% MC and between 20°C and 80°C, respectively. An adjustment of measured MOE to the ideally tangential direction was made by using correction factors calculated from finite element simulations. The results show MOE and the gradients with respect to MC and temperature and how they vary with MC and temperature. The gradients are factors in gradient terms in the incremental stress-strain relation for linear elastic behaviour during load cycles where there are mechanical loads and at the same time varying MC and temperature. The gradient terms add to the temperature and MC expansion coefficients and may be of significant size for cases with high stress, high temperature and high MC.Validerad; 2012; 20120807 (matse

Impact of laminate directions on inplane shear stiffness of crosslaminated timber

Twenty-three finite element models of cross-laminated timber (CLT) with different laminate directions were studied. Simulations with quadratic orthotropic linear elastic finite elements were conducted. One goal was to compare in-plane shear stiffnesses for CLT blocks made up from Norway Spruce (Picea abies) boards. 3- and 5-layer CLT were studied with board sizes 25x150x1200 mm. Bloc sizes were 75x1200x1200 and 125x1200x1200 mm for 3-layer and 5-layer blocs, respectively. The first and last layers laminate directions were assumed to be in direction 0○. The second and fourth layers laminate directions for 5-layer models were assumed equal and were 5○, 10○, 15○, 30○, 45○, 60○, 75○ and 90○. The middle layer was in direction 0○ or 90○. For 3-layer models the middle layers laminate directions were 5○, 10○, 15○, 30○, 45○, 60○, 75○ and 90○. No edge gluing was assumed and thus all side edges were allowed to separate or overlap. Glued contact surfaces were assumed to be perfectly glued with rigid glue. The results for 5-layer models showed that all models with angled second and fourth layers were stiffer than the models with 90○ layers. Stiffnesses for models with angled second and fourth layers were higher when the middle layer laminate direction was 90○ compared to 0○. The stiffest 5-layer model was the one with laminate directions 0/45/90/45/0. This stiffness was 1.5 times the shear stiffness of a reference block with 1-layer and solid timber shear stiffness. The stiffest 3-layer model was the one with laminate directions 0/30/0. This stiffness was 0.99 times the shear stiffness of the reference bloc

Finite Element Simulation of Nailed Glulam Timber Joints

hispaper presents a finite element modeling method for a certain type of nailed jointbetween glulam beams. The joint in question is a traditional arrangement of a horizontal beam anda vertical pillar but herethere is also a nailed steel plate inserted on the two sides in order to strengthen the joint.Experimental results and a comparisonsof simulated and experimental results aremade. The model includes the elastic and plastic orthotropic behaviour of wood and the elastic and plastic behaviour of nails.The nail joint between the steel plate and the wood is modelled as an elastic-plastic surface to surface connection with elastic-plastic properties. Also the reinforcing effect of nails in the nail-affectedvolume of wood is taken into consideration by raising rolling shear yield limitin the affected wood volume.The comparisons showthat the model works well and give results that are comparable to experimental results.Validerad; 2016; Nivå 1; 20151221 (andbra)</p

Shear resistance of glulam beams with cracks

Godkänd; 2012; 20121109 (andbra

Finite Element Models for Stress-Laminated Solid Wood Decks

Stress laminated timber bridge decks consist of planks or glulam timber members that are put together side by side to form plates or solid volumes of wood to be used as bridge decks. The decks may also be used for other purposes than bridge decks. Load-carrying capacities of these decks are very high and friction alone carries load between individual members. Friction is achieved by using prestressed steel rods through the decks that give normal compressive forces between members, see Fig.1. Fig.1. Left: bridge deck in laboratory test situation. Right: FE modelThe load vs. displacement curve for a transversally loaded deck is normally nonlinear even for low load values but especially for high loads due to partial slip between members. FE simulations and laboratory tests for behaviour have been made earlier, see [1], [2], [3]. Two different approaches for FE-simulations have been used, one with an elastic-plastic material model without discrete member modeling and another with discrete member modeling and contact surfaces between members.In the presentation a summary of earlier results are shown and also some recent results due to additional features in the FE models. The additions are possibilities too simulate gaps between members for the elastic-plastic model and results from butt-end modeling with the contact model. Fig. 2 shows an example of a non-linear load vs. displacement curve for a model with butt-end joints in the deck.Fig.2. load vs. displacement curve for a model with butt-end joints in the deck.References[1] Ekevad M.; Jacobsson P.; Forsberg G. (2011). Slip between glulam beams in stress-laminated timber bridges: finite element model and full-scale destructive test. Journal of Bridge Engineering 16:188-196.[2] Ekholm K.; Ekevad M.; Kliger R. (2014). Modelling slip in stress-laminated timber bridges: comparison of two FEM approaches and test values. Journal of Bridge Engineering 19(9) 04014029.[3] Ekevad M.; Jacobsson P.; Kliger R. (2013). Stress-Laminated Timber Bridge Decks: Non-linear Effects in Ultimate and Serviceability Limit States. International Conference on Timber Bridges 2013 (ICTB2013). Arranged by USDA Forest Products Laboratory. Las Vegas, USA, September 30-October 2, 2013.Godkänd; 2015; 20150625 (matse)</p