Analysis of layered wooden shells using an orthotropic elasto-plastic model for multi-axial loading of clear spruce wood

The analysis of layered wooden shells requires a suitable constitutive model for multi-axially loaded wood. This paper presents a sophisticated model for softwood suitable for the description of inelastic deformations both in-plane and transverse to the shell surface. It incorporates micromechanical failure mechanisms in an orthotropic single-surface formulation by means of a non-associative hardening/softening law. The latter permits identification of active failure mechanisms and control over six distinct strength functions. These strength functions are used for the definition of a deformable elliptical state surface.Special issues concerning an effective numerical implementation of the proposed model are discussed. The return mapping algorithm is adopted for this purpose. It remains fully functional and effective for the orthotropic model with its non-conventional hardening/softening behavior. Moreover, the consistent tangent can be given as a closed form expression.Applicability of the model is verified by the finite element analysis of a layered cylindrical shell with one opening and stiffeners.