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The finite difference approximation is applied to estimate the moisture-dependent diffusion coefficient by utilizing test data of isothermal moisture desorption in northern red oak (Quercus rubra). The test data contain moisture distributions at discrete locations across the thickness of specimens, which coincides with the radial direction of northern red oak, and at specified times. Also, the rate of moisture variation at each specified time and location must be known or correctly esti mated. The functional form of the diffusion coefficient as well as the boundary conditions at the surfaces are not known a priori. The resulting system of finite difference equations defines an inverse problem, whose solution may be sensitive *Corresponding author. E-mail: jliu@fs.fed.us † The Forest Products Laboratory is maintained in cooperation with the University of Wisconsin. This article was written and prepared by U.S. Government employees on official time, and it is therefore in the public domain and not subject to copyright. 1555Published by Marcel Dekker, Inc.www.dekker.com LIU, SIMPSON, AND VERRILLto small changes of input data. Results indicate that the diffu sion coefficient increases with increasing moisture content below the fiber saturation point, which defines the upper limit applied by the diffusion theory.

This report describes a mathematical model for fatigue strength of cellulosic materials under sinusoidal loading. The model is based on the Reiner-Weissenberg thermodynamic theory of strength in conjunction with a nonlinear Eyring’s three-element model. This theory states that failure depends on a maximum value of the intrinsic free energy that can be stored elastically in a volume element of the material. The three-element mechanical model, which consists of a linear spring in series with a parallel array of another linear spring and an Eyring dashpot, provides a good description of rheological material properties. The strength model system was able to predict rupture occurrence of polymers and wood structural members under constant and ramp loading with satisfactory results. For sinusoidal loading, the present study shows that the strength model system can predict time at fracture as a function of applied mean stress, amplitude of cyclic stress, and stress frequency. Numerical examples with model parameters evaluated for small Douglas-fir beams are presented.

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