Material-Response-Informed DeepONet and its Application to Polycrystal Stress-strain Prediction in Crystal Plasticity

Abstract

Crystal plasticity (CP) simulations are a tool for understanding how microstructure morphology and texture affect mechanical properties and are an essential component of elucidating the structure-property relations. However, it can be computationally expensive. Hence, data-driven machine learning models have been applied to predict the mean-field response of a polycrystal representative volume element to reduce computation time. In this work, we proposed a novel Deep Operator Network (DeepONet) architecture for predicting microstructure stress-strain response. It employs a convolutional neural network in the trunk to encode the microstructure. To account for different material properties, boundary conditions, and loading, we proposed using single crystal stress-strain curves as inputs to the branch network, furnishing a material-response-informed DeepONet. Using four numerical examples, we demonstrate that the current DeepONet can be trained on a single material and loading and then generalized to new conditions via transfer learning. Results show that using single crystal responses as input outperforms a similar model using material properties as inputs and overcomes limitations with changing boundary conditions and temporal resolution. In all cases, the new model achieved a $R^2$ value of above 0.99, and over 95\% of predicted stresses have a relative error of $\le$ 5\%, indicating superior accuracy. With as few as 20 new data points and under 1min training time, the trained DeepONet can be fine-tuned to generate accurate predictions on different materials and loading. Once trained, the prediction speed is almost $1\times10^{4}$ times faster the CP simulations. The efficiency and high generalizability of our DeepONet render it a powerful data-driven surrogate model for CP simulations in multi-scale analyses.