A surrogate model for studying random field energy release rates in 2D brittle fractures

TL;DR

This paper introduces a weighted-variational surrogate model for simulating brittle fractures with random energy release rates, significantly reducing computational time while maintaining accuracy, enabling efficient Monte Carlo studies.

Contribution

The paper presents a novel weighted-variational model using Gaussian random fields to efficiently approximate brittle fracture simulations, reducing computation time by 90%.

Findings

Weighted-variational model reduces execution time by 90%.

Model accurately mimics hybrid phase-field fracture simulations.

Enables efficient Monte Carlo analysis of fracture behavior.

Abstract

This article proposes a weighted-variational model as an approximated surrogate model to lessen numerical complexity and lower the execution times of brittle fracture simulations. Consequently, Monte Carlo studies of brittle fractures become possible when energy release rates are modelled as a random field. In the weighed-variational model, we propose applying a Gaussian random field with a Mat\'ern covariance function to simulate a non-homogeneous energy release rate ($G_c$) of a material. Numerical solutions to the weighed-variational model, along with the more standard but computationally demanding hybrid phase-field models, are obtained using the FEniCS open-source software. The results have indicated that the weighted-variational model is a competitive surrogate model of the hybrid phase-field method to mimic brittle fractures in real structures. This method reduces execution times by 90\%. We conducted a similar study and compared our results with an actual brittle fracture laboratory experiment. We present an example where a Monte Carlo study is carried out, modeling $G_c$ as a Gaussian Process, obtaining a distribution of possible fractures, and load-displacement curves.