# Three-dimensional Dipole BEM formulation for Cohesive Crack Propagation Modelling

## Palavras-chave:

Dipole Boundary Element Method, Three-dimensional crack growth, Nonlinear Fracture Mechanics## Resumo

This work presents a boundary element method (BEM) formulation for cohesive crack propagation

analysis in a 3D approach. BEM is a well-known and remarkable approach in fracture mechanics, providing

effective stress concentration modelling in addition to less complex remeshing procedures during crack growth.

The fracture effects are captured by using an alternative BEM formulation based on introducing a set of self-

equilibrated forces, called a dipole, which describes the cohesive zone. This BEM formulation demonstrates some

advantages in comparison to the classical DBEM approach. The DBEM solves the fracture problem with the

discretization of both crack surfaces, which leads to six integral equations (three displacements and three tractions)

per a couple of points at the crack surface. Alternatively, the dipole approach requires the discretisation of solely

one crack surface. Besides, the nonlinear solution scheme corrects the stress components solely at the FPZ, which

in the present case are three. Thus, the dipole approach requires solely three integral equations at the FPZ, which

is half compared to the DBEM. It leads to faster and more effective performance in terms of computational effort.

Some classic examples from the literature are presented in order to validate the 3D Dipole BEM formulation in

the light of cohesive crack propagation analysis. Finally, this proposal contributes toward advancing BEM in

engineering analyses, especially in nonlinear fracture mechanics.