On the mixed mode crack propagation using a 2D BEM formulation combined with a Newton-Raphson/Arc-length iterative method: discussion about material bifurcation

• An efficient criterion promotes the correct solution in the case where two directions can be associated with material bifurcation. • Fast convergence, even for complex benchmark tests. • Accurate BEM model identifies the right crack path for mixed mode fracture without crack pre-definition. Numerical modeling of mixed mode cracks propagation is discussed by using a 2D Boundary Element formulation with Quadratic convergence applied to Strong Discontinuities (BEMQ-SD). This model is based on strong discontinuity technique embedded into a continuum medium. The criterion for material bifurcation is the singularity of the acoustic tensor, being the normal direction to the crack surface defined by its eigenvalue. Usually only one direction is related to this singularity, but we discuss examples where we can have two different directions associated with the material bifurcation. Thus, we propose an efficient criterion to identify the correct solution. The Arc-length method combined with the Newton-Raphson method is adopted to obtain the solution of the iterative procedure required to solve the equilibrium problem. This force control procedure is efficient and has low computational cost, achieving the solution with a small number of iterations. As numerical examples, we consider a plate with a fragile sub-domain subjected to pure shear and to a combination of loads, a single-edge notched shear test and two experimentally tested examples, which present a mixed-mode fracture configuration with multiple cracks. We show that the proposed model can find the correct solution, and it is accurate, stable and efficient, showing itself to be an alternative tool to FEM or XFEM models. An important advantage of BEM models is that is not necessary to discretize the domain that remains with elastic behavior, what reduces the computational effort.