Probabilistic dipole BEM model for cohesive crack propagation analysis

This paper addresses the application of the boundary element method (BEM) to plane problems in probabilistic fracture mechanics. BEM stands out as an interesting technique for crack propagation analysis, leading to a robust modelling of stress concentration in singular regions, besides attenuating remeshing aspects. The alternative BEM formulation employed herein is built in terms of a set of self-equilibrated forces, called dipole, which describes the cohesive zone. Regarding the nonlinear solution, the tangent operator is used to make it faster. The probabilistic assessment of the crack propagation analysis is carried out in two stages: the first consists of a simulation-based estimation of the random values of cohesive parameters and elastic modulus, by an inferential approach; and in the second, the influence of these parameters on the structural response is evaluated. The statistical correlation between the random variables is taken into account. BEM models are coupled to structural reliability routines based on both first-order reliability method and Latin hypercube sampling-based Monte Carlo simulation to compute failure probabilities and random force versus displacement and crack path curves. Some examples are presented to validate the proposed models and to illustrate their efficacy on the reliability-based assessment of cohesive crack modelling.

Automated summary

This paper investigates the use of the boundary element method (BEM) for plane problems in probabilistic fracture mechanics. BEM is an interesting technique that allows for crack propagation analysis, accurately modeling stress concentration in singular regions, and avoiding remeshing issues. The alternative BEM formulation used in this study employs a set of self-equilibrated forces, called dipole, to describe the cohesive zone. The nonlinear solution is accelerated using the tangent operator. The probabilistic assessment of crack propagation analysis is conducted in two stages: simulation-based estimation of random values for cohesive parameters and elastic modulus, followed by evaluating their influence on the structural response. The statistical correlation between random variables is taken into account. BEM models are coupled with structural reliability routines to compute failure probabilities, as well as random force-displacement and crack path curves.