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

TL;DR

This paper addresses the computational bottleneck of crystal plasticity simulations by introducing a material-response-informed DeepONet (SC-DeepONet) that predicts mean-field stress–strain curves for polycrystal RVEs. The architecture uses a ResUNet trunk to encode microstructure and feeds 36 single-crystal stress–strain responses as the branch input, effectively forming a nonlinear rule of mixture that preserves physically meaningful binding of material properties and boundary conditions. Across four numerical scenarios, SC-DeepONet demonstrates near-perfect accuracy ($R^2>0.99$, >95% of predictions with relative error $\le 5\%$) and excellent transfer learning capabilities, achieving substantial data efficiency (as few as 20 new samples) and speed-ups of up to $10^4$× over full CP FE simulations. The approach provides a robust, scalable surrogate for multi-scale CP analyses and has potential for rapid ICME integration, with planned extensions to 3D RVEs and more complex microstructures.

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.

Figures (12)

• Figure 1: \ref{['basis']} Single crystal responses under tension. \ref{['basis_avg']} A typical polycrystal RVE response in tension compared to the Voigt and Reuss approximations computed from all single crystal responses. \ref{['avg_strain']} Mean strain response of a typical polycrystal RVE and single crystals.
• Figure 2: Schematic of the proposed DeepONet.
• Figure 3: Four typical synthetic microstructures in the training data set, contour color is assigned based on Euler angle.
• Figure 4: \ref{['c1']} Aluminum under 1% tension. \ref{['c3']} Copper under 0.125% tension. \ref{['c2']} Aluminum under 2% shear. \ref{['c4']} Copper under cyclic loading.
• Figure 5: \ref{['hist']} Histogram of absolute stress error. Scatter plot comparing simulated and predicted stresses for: \ref{['mp_corr']} MP-DeepONet, \ref{['sc_corr']} SC-DeepONet.