Cohesive crack propagation modelling in wood structures using BEM and the Tangent Operator Technique

Mechanical collapse in a wide range of materials occurs due to the growth of internal discontinuities. Such discontinuities, commonly denominated cracks, are explained consistently according to fracture mechanics theory. When the fracture process zone in front of the crack tip is sufficiently large, nonlinear mechanical effects appear and cannot be neglected. To allow a robust and general mechanical representation of such nonlinear phenomena, numerical techniques are required. In this context, this study presents an efficient nonlinear solution technique coupled to algebraic Boundary Element Method (BEM) equations to model the crack propagation process in anisotropic quasi-brittle bodies, using wood as a particular case. This nonlinear technique, called the Tangent Operator (TO), incorporates the derivative set of constitutive nonlinear laws into the algebraic BEM equations. The proposed nonlinear formulation was applied in mechanical analyses involving multi-crack growth and crack propagation in anisotropic media. The numerical results obtained by BEM/TO were compared with experimental and numerical responses available in the literature. In addition to the accuracy observed, the TO demonstrated faster convergence when compared with the classical approach.