Abstract
When a wood board is exposed to a change in relative humidity on only one of its surfaces, e.g. in case of flooring or a panel painting, the resulting asymmetric moisture content profile induces differential expansion over the thickness. Consequently a bending moment causes the board to curve. A theory is presented to describe the bending of a wood board due to a step change in relative humidity. The board is assumed to be homogeneous, isotropic, and linearly elastic. Moisture transport is presumed to obey the diffusion equation with constant coefficients, such that moisture transport can be directly related to the bending of the board. It is shown that the transient deflective behavior provides the diffusion coefficient and the final length change yields the linear hygroscopic expansion coefficient. Derived diffusion coefficients are in good agreement with values in literature. Furthermore, a scaling law for the deflection of the board is proposed, which is seen to be followed qualitatively but not quantitatively by experiments. Finally, by assuming the deflection of the board to be the response of a linear system, the deflective frequency response of the board can be predicted from its step response. The results allow upscaling of deflection and expansion, such that behavior of thick boards can be determined from an experiment using a thin board.
Highlights
The shape change due to moisture sorption is a familiar phenomenon in natural systems
A simple theory is proposed based on the diffusion equation and linear elasticity to analyze experiments with oak boards exposed unilaterally to moisture
The diffusion coefficient and linear hygroscopic expansion coefficient of wood can be derived which are in agreement with literature values
Summary
The shape change due to moisture sorption is a familiar phenomenon in natural systems. Due to the bilayered structure of the individual scales, a change in the relative humidity of the ambient air causes differential expansion of the two layers. As these two layers are firmly attached to each other this will result in a bending moment, thereby opening the cone. Another well-known example of a hygromorphic material is wood. The resulting change in moisture content of the wood leads to expansion or shrinkage, as the fibers which constitute
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