Machine Learning of Dislocation-Induced Stress Fields and Interaction Forces
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https://doi.org/10.1007/s11837-020-04389-w Ó 2020 The Minerals, Metals & Materials Society
AUGMENTING PHYSICS-BASED MODELS IN ICME WITH MACHINE LEARNING AND UNCERTAINTY QUANTIFICATION
Machine Learning of Dislocation-Induced Stress Fields and Interaction Forces MOHAMMAD H. RAFIEI,1,2 YEJUN GU,1 and JAAFAR A. EL-AWADY
1,3
1.—Department of Mechanical Engineering, Whiting School of Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA. 2.—e-mail: [email protected]. 3.—e-mail: [email protected]
In discrete dislocation dynamics (DDD) simulations dislocation-induced stress fields and dislocation–dislocation interaction forces are typically evaluated using analytically described multiparameter continuous functions. The universal approximation theory guarantees the approximation of such functions by some machine learning (ML) techniques, which in turn can potentially help to accelerate DDD simulations. However, accurate machine approximation is as crucial as its acceleration. Here, we demonstrate the feasibility of utilizing deep neural networks to predict dislocation-induced stress fields and dislocation–dislocation interaction forces. We also show that the trained network produces estimates that are in very good agreement with analytical solutions. This was only plausible by generating an enriched data repository to avoid bias in the training data. This work opens the door to further development of more optimized ML architectures that could lead to a more computationally efficient, yet accurate, approach to replace the generally inefficient analytical calculations of dislocation–dislocation interaction forces in DDD simulations.
INTRODUCTION Significant advances have been made in recent years to enrich existing multiscale materials simulation methods at different length/time scales to capture physics-based phenomena, including the different complexities associated with material microstructure and defects, and their mutual interactions/evolution. While multiscale simulation methods have led to a wealth of data and predictions over the past decade, there are still significant challenges that inhibit the full utilization of integrated multiscale materials methods in materials design and prediction of deformation and failure. These challenges include difficulties in accelerating such simulations and linking scales due to mismatch between the length/time scales of different models. Additionally, there are inherent difficulties in identifying which data to pass and identifying the quantitative distributions or the critical contribution of the tails of these distributions.
(Received July 2, 2020; accepted September 14, 2020)
With recent advances in machine learning (ML) and the principles of informatics, such challenges can potentially be overcome.1 In particular, machine learning (ML) is perhaps one of the most important technologies that can help accelerate computationally intensive materials simulations,2,3 estimations,4–6 design,7–11 and discovery.12–15 Discrete dislocation dynamics (DDD) simulations prov
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