Material properties are inevitably stochastic due to the manufacturing process and the measurement procedure. In case of a cracked domain, the stochasticity of material properties (as stochastic variables) may manifest in the stress intensity factors (SIFs). Having the stochastic representation of the material properties, Young modulus and Poisson ratio (isotropic material), we approximate the SIFs for 2D cracked domains using the generalized polynomial chaos (gPC). The approximated SIF consists of two families of orthogonal polynomials, selected by the probability distribution function of the material properties. The polynomials are multiplied by a deterministic coefficient, consisting of deterministic SIFs, extracted from a finite element model according to the stochastic properties of both Young modulus and Poisson ratio. Numerical example problems are provided where the stochastic approximation of the SIF is computed. The obtained approximation of the SIF is compared with results obtained using the Monte Carlo method. The results demonstrate the efficiency and accuracy of the proposed method.

由于制造过程和测量程序的原因，材料特性不可避免地是随机的。在开裂域的情况下，材料特性的随机性（作为随机变量）可能体现在应力强度因子（SIF）中。具有材料特性，杨氏模量和泊松比（各向同性材料）的随机表示，我们使用广义多项式混沌（gPC）来近似二维裂化域的SIF。近似的SIF由两个正交多项式族组成，这两个正交多项式由材料属性的概率分布函数选择。多项式乘以确定系数，该系数由确定性SIF组成，并根据杨氏模量和泊松比的随机特性从有限元模型中提取。提供了计算SIF随机近似值的数值示例问题。将获得的SIF近似值与使用Monte Carlo方法获得的结果进行比较。结果证明了该方法的有效性和准确性。