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Machine Learning Applied to Prediction of Brittle Fracture Processes

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Dear Colleagues,

In recent decades, simulation of brittle fracture and fragmentation processes have been addressed with the help of high-fidelity first-principle physics-based numerical models which rely on different solution methodologies (e.g., finite elements). Similarly, the emergence of experimental capabilities now allows for detailed and in situ material characterization. As a consequence, the evolution of individual cracks and crack networks inside a brittle medium can be studied with a high level of fidelity at a microscale level. However, high-fidelity models can be quite expensive from the point of view of the CPU resources and the time needed to obtain a solution, to a point in which they can seriously constrain the simulation scale addressable. Furthermore, the sensitivity of the chosen numerical model with respect to the input parameters and the boundary conditions of the systems is not always clear to the user, which can have serious consequences when trying to establish error bounds for the obtained solutions. From an experimental standpoint, these techniques result in very large, multi-dimensional datasets that take time to process and study. An alternative approach is to develop machine learning techniques to learn from experimental datasets and/or from numerical results obtained from high fidelity numerical simulations, in order to obtain reasonable answers in a fraction of the time and resources needed with the other alternatives, thus accelerating the discovery and optimization of new/current material systems.

This Special Issue concentrates on gathering the latest and greatest advances in the application of machine learning techniques to the resolution, study, and classification of fracture processes (initiation, propagation, arrest, interaction, etc.) in brittle materials. Original contributions from engineers, mechanical materials scientists, computer scientists, physicists, chemists, and mathematicians are encouraged. Both experimental and theoretical papers are welcome.

Dr. Esteban Rougier
Dr. Abigail Hunter
Guest Editors

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21 pages, 1502 KiB

Open AccessArticle

Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials

by Maruti Kumar Mudunuru, Nishant Panda, Satish Karra, Gowri Srinivasan, Viet T. Chau, Esteban Rougier, Abigail Hunter and Hari S. Viswanathan

Appl. Sci. 2019, 9(13), 2706; https://doi.org/10.3390/app9132706 - 3 Jul 2019

Cited by 17 | Viewed by 3427

Abstract

In brittle fracture applications, failure paths, regions where the failure occurs and damage statistics, are some of the key quantities of interest (QoI). High-fidelity models for brittle failure that accurately predict these QoI exist but are highly computationally intensive, making them infeasible to incorporate in upscaling and uncertainty quantification frameworks. The goal of this paper is to provide a fast heuristic to reasonably estimate quantities such as failure path and damage in the process of brittle failure. Towards this goal, we first present a method to predict failure paths under tensile loading conditions and low-strain rates. The method uses a k-nearest neighbors algorithm built on fracture process zone theory, and identifies the set of all possible pre-existing cracks that are likely to join early to form a large crack. The method then identifies zone of failure and failure paths using weighted graphs algorithms. We compare these failure paths to those computed with a high-fidelity fracture mechanics model called the Hybrid Optimization Software Simulation Suite (HOSS). A probabilistic evolution model for average damage in a system is also developed that is trained using 150 HOSS simulations and tested on 40 simulations. A non-parametric approach based on confidence intervals is used to determine the damage evolution over time along the dominant failure path. For upscaling, damage is the key QoI needed as an input by the continuum models. This needs to be informed accurately by the surrogate models for calculating effective moduli at continuum-scale. We show that for the proposed average damage evolution model, the prediction accuracy on the test data is more than 90%. In terms of the computational time, the proposed models are

\approx O (10^{6})

times faster compared to high-fidelity fracture simulations by HOSS. These aspects make the proposed surrogate model attractive for upscaling damage from micro-scale models to continuum models. We would like to emphasize that the surrogate models are not a replacement of physical understanding of fracture propagation. The proposed method in this paper is limited to tensile loading conditions at low-strain rates. This loading condition corresponds to a dominant fracture perpendicular to tensile direction. The proposed method is not applicable for in-plane shear, out-of-plane shear, and higher strain rate loading conditions. Full article

(This article belongs to the Special Issue Machine Learning Applied to Prediction of Brittle Fracture Processes)

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