Finite Element Modeling Of The Hygroscopic Warping Of Medium Density Fiberboard

Stefan Ganev, Alain Cloutier, Guy Gendron, Robert Beauregard


The objective of this study was to develop a three-dimensional finite element model of the hygromechanical deformation of medium density fiberboard (MDF) panels with various vertical density profiles subjected to moisture adsorption on one face. The theoretical model was based on three sets of equations: 1) three-dimensional equations of unsteady-state moisture diffusion, 2) three-dimensional equations of mechanical equilibrium, and 3) Hooke's law for plane isotropy, which takes into account shrinkage and swelling through the panel thickness. The finite element model was applied to six panels with various density profiles. For both the simulations and the experiments, the warping was caused by moisture adsorption from one of the faces of 560-mm x 560-mm x 12-mm MDF panels while the other surface and the edges were sealed. Physical and mechanical characteristics defined as a function of density and moisture content were used as model inputs. The model made it possible to capture the rapid initial development of maximum warp and its following decrease as moisture content equalized through panel thickness; the effect of the density profile on the level of warp caused by moisture adsorption; and warp fluctuations resulting from changes in the ambient relative humidity, and from the hysteresis in the expansion coefficient between adsorption and desorption. To validate the model, the warp development of laboratory MDF panels was compared to simulation results. The agreement between calculated and actual panel warping confirmed that the model could successfully be used to simulate moisture movement in MDF and the resulting warp, and to help in the optimization of panel vertical density profiles aiming at better stability of form in MDF panels. For the typical experimental cases, it was observed that there was a strong effect of panel density profile on the levels of warp and its dynamics. The levels of warp increased with average panel density. The panels with sharper density profile developed stronger warp compared to panels with an even profile. When the density profile was skewed towards one of the surfaces, the panel developed positive or negative warp and did not return to the original flat form.


MDF (medium density fiberboard);hygromechanical warping;finite element model;elastic properties;density profile;moisture diffusion

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