Three-dimensional constitutive modelling of arbitrarily orientated timber based on continuum damage mechanics

An orthotropic constitutive model is developed in order to capture the complex response of unidirectional fibrous materials with arbitrary orientation under a three-dimensional (3D) stress state. Different modes of failure and their associated criteria are derived via decomposition of a single-surface yield function in the fibre and matrix directions. The uniaxial behaviour of each stress component is approximated by a multi-linear model, and the concepts of continuum damage mechanics are utilised to model the degradation of various components under a general 3D stress state. The proposed model is implemented as a user material subroutine in ABAQUS®, and it is utilised to analyse the non-linear mechanical response of bulk or laminated timber. The crack band model and the viscous regularisation techniques are employed to alleviate the spurious mesh sensitivity and convergence problems in the softening state. Some benchmark and practical examples are presented to verify the accuracy and performance of the proposed model for predicting different modes of failure and non-linear behaviour with respect to orientation of the fibres and loading.