Reliability analysis of the stress intensity factor using multilevel Monte Carlo methods

This paper presents a reliability analysis for fracture toughness using a multilevel refinement on a hierarchy of computational models. A 2D finite element model discretized by quadrilateral elements is developed to analyze the stress intensity with the presence of an initial edge crack. The multilevel simulations are obtained considering a non-uniform sequence of mesh refinement in the vicinity of the crack tip. We set the probabilistic problem accounting for applied stress and crack size uncertainties. We analyze several error tolerances using the standard and multilevel Monte Carlo methods combined with the selective refinement procedure. The probability of failure is estimated by expanding it in a telescoping sum of an initial approximation at the coarsest mesh and a series of incremental corrections between the subsequent levels. In our analysis, we take on two common fracture problems; a single-edge notched tension to investigate the pure mode-I and an asymmetric four-points bending to consider the mixed mode-I/II. The results show significant savings in the computation cost.