Mathematical modeling to predict drying deformation and stress due to the differential shrinkage within a tree disk

Abstract

Although many mathematical models for wood drying have been developed to predict the drying behavior of lumber, there were limited results on drying models dealing with tree disks. This study attempted to try to develop mathematical models to predict the drying stresses and crack formation in a tree disk assumed as a cylindrically orthotropic material with radial variations of properties. The results showed that the drying stress changes nonlinearly with decreasing moisture content (MC) due to mechano-sorptive effects. The higher the orthotropic properties of tree disks are, the larger the drying stress occurs. The developed mathematical model showed that the pattern of cracks such as V-crack or heart check significantly depended on the MC distribution along the radial direction. The model also indicated that a dominant factor controlling the drying behavior of tree disk was the differences in MC between heartwood and sapwood within a tree disk of a given species without any chemical or mechanical treatments.