Microstructure sensitive recurrent neural network surrogate model of crystal plasticity

TL;DR

This work addresses the computational bottleneck of full-field crystal plasticity (CP) simulations by introducing a microstructure-informed GRU-based surrogate that maps 3D grain structures and deformation histories to homogenised stress. The approach uses two microstructure projections to initialise the GRU state and augment inputs, enabling path-dependent predictions across diverse microstructures, trained on a large CP dataset generated with random Voronoi microstructures. The surrogate reproduces CP predictions with 2–3 MPa error on in-distribution data and demonstrates potential to replace constitutive updates in FE2-like workflows, delivering substantial runtime gains. Textured or out-of-distribution microstructures require targeted training data, but the results establish a viable route toward fast, microstructure-aware multiscale modelling with uncertainty quantification.

Abstract

The development of next-generation structural materials for harsh environments requires rapid assessment of mechanical performance and its dependence on microstructure. While full-field crystal plasticity (CP) models provide detailed insights, the high computational cost limits their use with uncertainty quantification workflows and in component-scale simulation. Surrogate models based on recurrent neural networks (RNNs) have shown promise in reproducing history-dependent mechanical behaviour but are applied to models with either fixed microstructure or representative volume elements. Here, we develop a microstructure sensitive RNN surrogate that predicts homogenised stress responses directly from three-dimensional grain structures and arbitrary deformation histories. The architecture employs a gated recurrent unit (GRU) with mappings from microstructure to both the initial hidden state and sequence inputs, allowing the model to capture path dependence and microstructure variability. Training data comprised of over 300,000 CP simulations generated using combinations of randomly generated microstructures and loading paths. The model was found to reproduce CP predictions for both in-distribution validation data and unseen deformation modes, with errors of 2 MPa to 3 MPa. Out-of-distribution microstructures were more difficult to predict, emphasising the need for representative training data with, for example, heavily textured microstructures. Embedding the model into a multiscale framework demonstrates its ability to replace conventional constitutive updates, reducing computational cost while preserving key features of the stress distribution. These results establish microstructure-informed RNN surrogates as a promising alternative to direct CP simulations, offering a pathway toward rapid multiscale modelling and uncertainty quantification.

Figures (12)

• Figure 1: Network diagram of proposed surrogate model. The left section is a mapping from microstructure parameters (grain locations and orientations) to a state vector and the right the RNN mapping a sequence of average deformations to average stresses.
• Figure 2: A typical value from the training set for a) microstructure Voronoi tessellation shown in inverse pole figure (IPF) colouring along a <100> direction and b) a loading path, where crosses mark the sections of different strain rate.
• Figure 3: Minimum validation loss curves for varying parameters from the baseline in Table \ref{['tab:baseline_params']}.
• Figure 4: Stress prediction for a single training point for each set of network parameters considered and the true output from the CP simulation (yellow).
• Figure 5: Mean and standard deviation of stress error (Equation \ref{['eqn:stressError']}) over the validation set plotted over sequence step for each set of network parameters considered.