Numerical Prediction of Engineered Wood Flooring Deformation

Dimensional stability is of primary importance in the use of layered wood composites such as engineered wood flooring. It is largely due to the physical and mechanical properties and moisture content changes of each layer. Therefore, the non-homogeneous adsorption or desorption of moisture by the composite may induce its deformation, thus decreasing product value. The objective of this study was to develop a finite element model of the hygromechanical cupping in layered wood composite flooring. The model is based on two sets of equations: 1) the three-dimensional equations of unsteady-state moisture diffusion, and 2) the three-dimensional equations of elasticity including the orthotropic Hooke's law, which takes into account the shrinkage and swelling of each layer. The proposed model was used to predict the deformation of an engineered wood flooring strip following desorption by the top surface. The model was solved by the finite element method, and the calculated cupping was validated against experimental data. The results show that the proposed model can be successfully used to simulate the non-homogeneous moisture movement and the resulting cupping deformation in layered wood composites such as engineered wood flooring strips. For both predicted and measured deformation, roughly 80% of the cupping deformation appears after 3 days of conditioning. The low water vapor diffusion coefficient of the urea-formaldehyde film used between the surface and core layers of the strip plays a key role in the deformation process. After 42 days of conditioning, the model results overestimated the experimental results by 12% but were within one standard deviation of the experimental results. The model presented in this study appears to be a useful tool for product design purposes

Topology of Hitchin systems and Hodge theory of character varieties: the case A_1

For G = GL_2, PGL_2 and SL_2 we prove that the perverse filtration associated to the Hitchin map on the cohomology of the moduli space of twisted G-Higgs bundles on a Riemann surface C agrees with the weight filtration on the cohomology of the twisted G character variety of C, when the cohomologies are identified via non-Abelian Hodge theory. The proof is accomplished by means of a study of the topology of the Hitchin map over the locus of integral spectral curves.Comment: 67 pages, arguments streamlined, to appear in Annals of Mathematic