A multi-surface plasticity model for clear wood and its application to the finite element analysis of structural details

Recent biaxial experiments on spruce wood show that consideration of an elliptic failure surface according to Tsai and Wu, and of an elastic model for stress states within this envelope, gives an insufficient description of the mechanical behavior. As compression perpendicular to grain occurs, a nonlinear stress path results from a proportional biaxial strain path. Moreover, a phenomenological single-surface model does not permit easy identification of failure modes and thus renders the description of different post-failure mechanisms very difficult. Investigation of characteristic samples for various biaxial loading conditions enables the identification of four basic mechanisms covering the behavior of wood under plane stress conditions. The experimentally observed mechanical behavior will be described by means of a multi-surface plasticity model. It consists of four surfaces representing four basic failure modes. The first is a modified tension cut-off for the description of fiber rupture. The second is a mixed mode radial tension-shear model by Weihe applied to the perpendicular to grain direction. The third is an extension of the authors' prior model for perpendicular to grain compression, and the fourth surface covers the compressive failure parallel to grain. The model represents the orthotropic multi-surface elasto-plastic material clear wood. The aim of this paper is to present and discuss selected experimental data from biaxial tests with respect to distinct failure modes, and to develop an orthotropic plasticity model for its mathematical description. Since available experimental data cover only plane stress in the LR-plane,(1) both orthotropic failure and yield surfaces, respectively, are restricted to this case.