Probabilistic modeling and numerical simulation of the three-point bending behavior of wooden beams

This paper presents a simplified yet realistic numerical model, based on a uniform probabilistic law and Monte Carlo simulations, to investigate the failure behavior of wood in static three-point bending.The proposed approach replaces the real heterogeneous beam with a geometrically idealized beam composed of multiple perfectly bonded lamellae with well-defined geometric properties, whose mechanical properties are randomly generated according to a uniform probabilistic distribution. By combining the fundamental equations of statics with mathematical expressions derived from uniform probability distributions, a simulation algorithm is developed to study beam failure under three-point bending. Numerical results are in qualitative agreement with findings reported in the literature. The obtained force-displacement and damage- displacement curves, combined with a rigorous statistical analysis, highlight the dispersive nature of the mechanical behavior of wooden beams under bending, thereby allowing for better control of their inherent biological variability. Furthermore, the stress-size relationships confirm the relevance of Bažant’s size effect law in characterizing the flexural response of wood.