A stochastic perturbation study for 2D brittle fractures via a weighted-variational model

The study of fracture propagation is an essential topic for several disciplines in engineering and material sciences. Different mathematical approaches and numerical methods have been applied to simulate brittle fractures. Materials, naturally, present random properties that contribute its physical properties, durability, and resistance, for this reason, stochastic modeling is critical to obtain realistic simulations for fractures. In this research, we propose applying a Gaussian random field with a Matérn covariance function to simulate a non-homogeneous energy release rate (Gc) of a material. We propose a surrogate mathematical model based on a weighted-variational model to reduce numerical complexity and execution times for simulations in the hybrid phase-field model. The FEniCS open-source software is used to obtain numerical solutions to the variational and hybrid phase-field models with Gaussian random fields on the parameter Gc. Results have shown that the weighted-variational model as a surrogate model is a competitive tool to reproduce brittle fractures for real structures, reducing execution times by 90%.