Fractal finite-element based continuum shape sensitivity analysis of cracks

Probabilistic fracture mechanics (PFM) that blends the theory of fracture mechanics and the probability theory provides a more rational means to describe the actual behavior and reliability of structures. However in PFM, the fracture parameters and their derivatives are often required to predict the probability of fracture initiation and/or instability in cracked structures. The calculation of the derivatives of fracture parameters with respect to load and material parameters, which constitutes size-sensitivity analysis, is not unduly difficult. However, the evaluation of response derivatives with respect to crack size is a challenging task, since it requires shape sensitivity analysis. Using a brute-force type finite-difference method to calculate the shape sensitivities is often computationally expensive, in that numerous repetitions of deterministic finite element analysis may be required for a complete reliability analysis. Therefore, an essential need of probabilistic fracture-mechanics is to evaluate the sensitivity of fracture parameters accurately and efficiently. Copyright © 2007 by ASME.