Orthotropic Localizing Gradient Damage Model for Timber Based on an Extended Hashin Failure Criterion

This paper presents a new approach to the quasi-brittle damage analysis of timber due to quasi-static tensile and shear loading. The proposed model is developed by utilizing the localized gradient approach from continuum damage theory. The model incorporates damage through three distinct damage variables corresponding to orthogonal principal material directions of timber. A fourth-order tensor transformation is incorporated to enable conversions between global and local reference frames, thereby accommodating any spatial orientation of the matrix material. The model is formulated as a consistent linearized partwise coupled (monolithic) and partwise staggered problem. The model is applied to two numerical examples demonstrating its effectiveness in capturing damage propagation in the case of damage of complex timber structures. Furthermore, the results demonstrate the model’s advantage in predicting the damage initiation for different orientations of the orthogonal timber material directions in the structure.