Modelos probabilísticos para análise de propagação de fissuras em meios coesivos via método dos elementos de contorno

Abstract

This work deals with the use of formulations of the Boundary Element Method (BEM) in fracture problems, in a probabilistic framework. The BEM is a suitable method for solving these types of problems, since the absence of a domain mesh translates into a more efficient modeling of regions with high concentration of stresses. Besides, reducing the dimensionality of the mesh results in a convenient remeshing process. Regarding the non-linear BEM formulation, na alternative to the classic dual formulation will be used, with the introduction of an initial stress field to represent the cohesive zone, based on the concept of dipoles. This formulation is particularly interesting because it is able to represent mathematically the presence of the Inelastic Process Zone (IPZ) with only three algebraic equations (equations related to stress correction) per source point located in the crack path. In contrast, dual formulation requires four algebraic equations (displacements and forces) per source point. As for the effects relevant to the non-linear system, two distinct iterative resolution algorithms will be used, Constant Operator (CO) and Tangent Operator (TO). When coupling with reliability models, only TO will be used because it presents satisfactory responses in a smaller number of iterations. Regarding the probabilistic analysis, two approaches are considered, the first refers to the direct coupling between the numerical model and a transformation method (HLRF / FORM), while the second consists of the most straightforward coupling using the Monte Carlo Method. The fracture parameters are treated as random. Finally, the Latin Hypercube sampling technique is also employed, as it presents better convergence rates. Some examples are presented to validate the use of dipole formulation in crack propagation analysis, in the light of structural reliability.