Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networks

2026-06-09

AI Summary

This work addresses the computational bottleneck in multiscale modeling arising from the expensive reconstruction of local stress fields in heterogeneous microstructures under nonlinear, path-dependent loading. The authors propose a hybrid approach coupling a Long Short-Term Memory (LSTM) network with a physics-informed Graph Neural Network (GNN). The LSTM encodes the macroscopic stress–strain history to capture constitutive behavior, while the GNN reconstructs high-resolution stress fields at each time step. A dynamic weighting strategy balances data fidelity and mechanical equilibrium constraints, and a relative weighting scheme combined with linear warm-up overcomes convergence difficulties caused by fixed weights in elastoplastic regions. The framework enables zero-shot transfer across different mesh types and resolutions without retraining, achieving a three-order-of-magnitude speedup over finite element simulations and maintaining a cumulative error of only 1.9% on loading paths twice the training length, thereby significantly enhancing both efficiency and generalization.

Abstract

Reconstructing local stress fields in heterogeneous microstructures under non-linear, history-dependent loading remains a major computational bottleneck in multi-scale simulations. We propose a coupled LSTM-GNN framework that links the temporal and spatial aspects of local stress field reconstruction. A Long Short-Term Memory network encodes macroscopic stress-strain sequences into a compact hidden state that captures the path-dependent constitutive response, while a physics-informed Graph Neural Network reconstructs the spatially-resolved stress field at each time step. We introduce a relative weighting strategy with linear warm-up to balance the data-driven reconstruction loss and a discrete divergence-based equilibrium penalty. This resolves the scale mismatch that prevents fixed-weight formulations from converging in the elasto-plastic regime. The model is trained on 10,000 non-proportional loading paths applied to a periodic plate-with-a-hole microstructure and von Mises elasto-plasticity. The model achieves three orders of magnitude speedup over finite element simulations and generalizes to loading sequences twice the training length, with 1.9% cumulative error. Because the graph relies on mesh connectivity instead of the specific element type, one trained surrogate can be applied directly without retraining to meshes with different element types and to both coarser and finer resolutions, while in all cases reproducing the high-fidelity quad-element FE field used during training. Indeed, the message passing characteristics inherent to GNN and MeshGraphNet architecture render the model mesh-agnostic. Analysis of the LSTM hidden states suggests a low-dimensional structure related to the internal state variables of the constitutive model.

Problem

• non-linear mechanics
• stress field reconstruction
• heterogeneous microstructures
• history-dependent loading
• multi-scale simulations

Innovation

• physics-informed GNN
• LSTM-GNN coupling
• mesh-agnostic surrogate
• non-linear stress reconstruction
• path-dependent constitutive modeling