Wood and moisture-induced strains in a large deformation setting in 3D

Detta är en Master-uppsats från Linnéuniversitetet/Institutionen för byggteknik (BY)

Sammanfattning: Many studies have previously been done on moisture-induced strains in wood. An in- finitesimal/engineering strain model has been used for most of these studies, which is often an accurate approximation for small rotations. However, if large deformations oc- cur, then fictive strains are obtained resulting from the simplified engineering strain.  This work aims to develop a finite element formulation for problems of moisture- induced strains in orthotropic materials based on the total Lagrangian approach, where large displacements and rotations are considered. This model is then used to examine static drying deformations and their effect on dynamic vibrations. A dynamic vibration test was also done to estimate the modulus of elasticity in the fibre direction. The pur- pose is to increase the understanding of moisture-induced strains in wood and also to emphasize the advantages of using a large deformation model.  To facilitate the understanding of large deformation theory, the implementation is first done for a 2D isotropic beam where static and dynamic simulations are made. Re- sults will be compared with a standard model based on engineering strains. For the static part, two types of wooden species are studied, radiata pine and Norway spruce, and com- pared with a previous research study [32] where engineering strain theory is used. The dynamical considerations are divided into a theoretical and an experimental part. The theoretical part analyzes the vibration of radiata pine and Norway spruce samples from a study by Cown and Ormarsson 2005 [32]. In the experimental part, three Norway spruce boards were analyzed.  The results from the numerical implementation showed, among other things, that by taking moisture-induced strains into account two additional properties, the matrix Gm and the vector Emf appear in the finite element formulation. It was concluded that by using a large deformation model the accuracy will increase without causing any extra computational costs.  The transient numerical mass flow analysis showed reasonable results although the sorption exchange rate has to be slightly higher than indicated by comparable measure- ments. For the dynamic part, the performed experiment showed a difference in response between the three Norway spruce species. It was shown that the frequency increases with distance from the pith and also with lower moisture content. The difference in vibration response between Norway spruce and radiata pine was analyzed based on boards from a study by Cown and Ormarsson 2005 [32]. The response for Norway spruce tends to show a higher frequency compared to radiata pine for the test performed in this investigation. This is mainly due to a higher modulus of elasticity and lower density for Norway spruce compared to radiata pine. 

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