2023 Volume 79 Issue 15 Article ID: 22-15030
The contribution of this study is to examine the computational efficiency of Stochastic Collocation method (SC method) for evaluating dispersion in crack propagation problems. One of the advantages of the SC method is the independence between stochastic and mechanical calculations like the Monte Carlo method (MC method). The other is that the orthogonality of the Lagrangian polynomial and Gaussian quadrature rule makes it computationally efficient enough to evaluate the dispersion in a few samples. To represent brittle fracture, we employ the cohesive traction force embedded damage-like constitutive law, which incorporates a cohesive zone model with an arbittrary material constitutive law in finite element analysis (FEA). The cohesive zone model is able to represent the stress release process associated with brittle crack propagation after the maximum principal stress reaches local tensile strength. Thus, the combination between the FEA and the SC method enables us to predict the variation in brittle crack propagation due to the uncertainty in the local tensile strength and critical energy release rate. In addition, Radial Basis Function interpolation (RBF interpolation) is employed to reproduce the spatial distribution of material constants due to its dispersion in a specimen. The capability of the SC method is demonstrated throughout assessment of brittle crack propagation in comparison with the result of MC method. The statistics of brittle crack propagation, which are caused from spatial dispersion of material constants in the specimen, is evaluated by the proposed method combined with RBF interpolation.
