Non-intrusive stochastic SBFEM for the uncertainty quantification of Stress Intensity Factors

Predictive modeling of crack initiation is of extreme interest to the engineering community.Within the context of elastic fracture mechanics, the Scaled Boundary Finite Element Method (SBFEM) has proven both efficient and accurate in estimating Stress Intensity Factors (SIFs).More specifically, the SBFEM allows for an analytical evaluation of the stress field as it approaches the crack tip while reducing the dimensionality of the numerical problem by one.In contrast to other methods, e.g., the FEM or the XFEM, no adjustments to the solution procedure are required, and SIFs can be conveniently extracted during post-processing.However, experimental observations on crack initiation are typically underlined by a significant statistical dispersion.This is mainly due to uncertainties arising from the geometry of the crack tip and the variability of the material properties due to e.g., inhomogeneities at the micro or meso-material scale.To this end, this study presents an efficient approach for estimating SIFs under uncertainty.A stochastic scaled boundary finite element method is developed, and the merits and bottlenecks of a non-intrusive implementation are investigated.Furthermore, a comparative study is performed vis--vis the discretization method employed to generate sample domains, i.e., the Expansion Optimal Linear Estimation (EOLE) and the Karhunen-Love Expansion (KL).