Parameter identification for phase-field modeling of brittle fracture in spruce wood

Understanding and predicting fracture mechanisms in complex anisotropic materials, such as spruce wood and other biological materials, is essential for structural applications requiring reliability and durability, particularly in the furniture industry. This paper presents a comprehensive two-step approach to identify the elastic and fracture/damage properties of spruce wood by combining numerical predictions from phase-field fracture simulations with experimental measurements from physical experiments. Uniaxial compression tests were conducted on 18 drilled spruce specimens, with displacement fields and critical crack initiation forces measured experimentally using Digital Image Correlation (DIC) techniques. An ad hoc phase-field model for brittle fracture, adapted to anisotropic elastic materials, was employed to numerically simulate crack initiation and propagation in spruce wood. The transversely isotropic elastic properties of spruce wood are identified using a modified Finite Element Model Updating (FEMU) method that incorporates displacement field and global reaction force measurements obtained in the linear elastic regime. The damage/fracture properties of spruce wood, in particular the critical energy release rate characterizing the fracture toughness, are determined through a classical FEMU-based optimization approach that consists of matching the experimental crack initiation forces identified from DIC residual fields and the numerical critical reaction forces predicted by phase-field simulations. The identified material parameters are consistent with values reported in the literature for spruce wood. Numerical results demonstrate the ability of the phase-field fracture model to accurately capture crack initiation forces and replicate the experimentally observed crack paths in perforated spruce specimens under compression. These findings provide valuable insights into the fracture behavior of wood and highlight the potential of phase-field modeling as a robust tool for characterizing and predicting failure in anisotropic elastic materials.