Accelerating High-Strain Continuum-Scale Brittle Fracture Simulations with Machine Learning

Abstract: Failure in brittle materials under dynamic loading conditions is a result of the propagation and coalescence of microcracks. Simulating this mechanism at the continuum level is computationally expensive or, in some cases, intractable. The computational cost is due to the need for highly resolved computational meshes required to capture complex crack growth behavior, such as branching, turning, etc. Typically, continuum-scale models that account for brittle damage evolution homogenize the crack network in some way, which reduces the overall computational cost, but can also neglect key physics of the subgrid crack growth behavior, sacrificing accuracy for efficiency. We have developed an approach using machine learning that overcomes the current inability to represent micro-scale physics at the macro-scale. Our approach leverages damage and stress data from a high-fidelity model that explicitly resolves microcrack behavior to build an inexpensive machine learning emulator, which runs in seconds as opposed to the high-fidelity model, which takes hours. Once trained, the machine learning emulator is used to predict the evolution of crack length statistics. A continuum-scale constitutive model is then informed with these crack statistics, speeding up the workflow by four orders of magnitude. Both the machine learning model and the continuum-scale model are validated against a high-fidelity model and experimental data, respectively, showing excellent agreement. There are two key findings. The first is that we can reduce the dimensionality of the problem, establishing that the machine learning emulator only needs the length of the longest crack and one of the maximum stress components to capture the necessary physics. Another compelling finding is that the emulator can be trained in one experimental setting and transferred successfully to predict behavior in a different setting.