Probabilistic Fracture Mechanics Using Fractal Finite Element Method

This paper presents probabilistic fracture-mechanics analysis of linear-elastic cracked structures subjected to mixed-mode (modes I and II) loading conditions using fractal finite element method (FFEM). The method involves FFEM for calculating fracture response characteristics; statistical models of uncertainties in load, material properties, and crack geometry; and the first-order reliability method for predicting probabilistic fracture response and reliability of cracked structures. The sensitivity of fracture parameters with respect to crack size, required for probabilistic analysis, is calculated using continuum shape sensitivity analysis. Numerical examples based on mode-I and mixed-mode problems are presented to illustrate the proposed method. The results show that the predicted failure probability based on the proposed formulation of the sensitivity of fracture parameter is accurate in comparison with the Monte Carlo simulation results. Since all gradients are calculated analytically, reliability analysis of cracks can be performed efficiently using FFEM.