Predicting Peak Stresses In Microstructured Materials Using Convolutional Encoder-Decoder Learning

Abstract

This work presents a machine learning approach to predict peak-stress clusters in heterogeneous polycrystalline materials. Prior work on using machine learning in the context of mechanics has largely focused on predicting the effective response and overall structure of stress fields. However, their ability to predict peak stresses -- which are of critical importance to failure -- is unexplored, because the peak-stress clusters occupy a small spatial volume relative to the entire domain, and hence requires computationally expensive training. This work develops a deep-learning based Convolutional Encoder-Decoder method that focuses on predicting peak-stress clusters, specifically on the size and other characteristics of the clusters in the framework of heterogeneous linear elasticity. This method is based on convolutional filters that model local spatial relations between microstructures and stress fields using spatially weighted averaging operations. The model is first trained against linear elastic calculations of stress under applied macroscopic strain in synthetically-generated microstructures, which serves as the ground truth. The trained model is then applied to predict the stress field given a (synthetically-generated) microstructure and then to detect peak-stress clusters within the predicted stress field. The accuracy of the peak-stress predictions is analyzed using the cosine similarity metric and by comparing the geometric characteristics of the peak-stress clusters against the ground-truth calculations. It is observed that the model is able to learn and predict the geometric details of the peak-stress clusters and, in particular, performed better for higher (normalized) values of the peak stress as compared to lower values of the peak stress. These comparisons showed that the proposed method is well-suited to predict the characteristics of peak-stress clusters.

arXiv commentTo appear in Mathematics and Mechanics of Solids

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