Influence of grain direction on the time-dependent behavior of wood analyzed by a 3D rheological model. A mathematical consideration

Abstract

AbstractA three-dimensional (3D) rheological model for an orthotropic material subjected to sustained load or deformation under constant climate has been mathematically formulated. The elastic and viscoelastic compliance matrices are symmetric, where the mathematical derivation of the latter is shown. The model is linear and requires constant numerical values for the elastic and viscoelastic material parameters. The model’s ability to predict the natural time-dependent response in three material directions simultaneously is demonstrated on a Douglas fir (Pseudotsuga menziesii) specimen subjected to a constant uniaxial tensile load. The material extends in a longitudinal direction and contracts in the transverse directions with time. The required material parameters are taken from the literature when possible, otherwise they are assumed. Furthermore, the influence of misalignment between the directions of observation and wood material directions on induced time-dependent strains is analyzed. The analyses show that the misalignment has a large effect on the material behavior. In some cases, the specimen under constant uniaxial tension even extends in the perpendicular transverse direction with time. The obtained results clearly demonstrate the high importance of considering the alignment of material directions precisely in order to be able to interpret the time-dependent behavior of wood correctly.