Direct extraction of stochastic stress intensity factors using generalized polynomial chaos

The stochastic approximation of the Stress Intensity Factors (SIFs) for cracked domains with traction free boundary conditions on the crack edges having stochastic material property (stochastic variable) is presented explicitly using the generalized Polynomial Chaos (gPC). Using a set of deterministic SIF extracted from finite element model according to the stochastic properties of the material property, we compute the stochastic approximation of the SIF as a set of orthogonal stochastic polynomials, multiplied by a deterministic combination of the extracted SIFs. The method provides a direct stochastic SIF approximation and does not require a stochastic representation of the stresses or the displacement. Numerical examples are presented in which we consider either a stochastic Young modulus or stochastic Poisson ratio with normal distribution as a random variable. The example problems are compared with the indirect gPC SIF extraction method and Monte-Carlo results. The results demonstrate the efficiency and accuracy of the proposed method.