[Paper Review] Prediction of local elasto-plastic stress and strain fields in a two-phase composite microstructure using a deep convolutional neural network

Indrashish Saha, Ashwini Gupta+1 more|arXiv (Cornell University)|Oct 29, 2023

Non-Destructive Testing Techniques4 citations

TL;DR

This paper proposes a 3D U-Net convolutional neural network to predict local elasto-plastic stress and strain fields in two-phase fiber-reinforced plastic (FRP) composites under a predefined loading-unloading path. Using a novel two-step training approach—first predicting strain fields, then using those to predict stress fields—the model achieves high accuracy (mean relative error <1.6% for strain, <5.9% for stress) and speeds up prediction by orders of magnitude compared to finite element methods.

ABSTRACT

Design and analysis of inelastic materials requires prediction of physical responses that evolve under loading. Numerical simulation of such behavior using finite element (FE) approaches can call for significant time and computational effort. To address this challenge, this paper demonstrates a deep learning (DL) framework that is capable of predicting micro-scale elasto-plastic strains and stresses in a two-phase medium, at a much greater speed than traditional FE simulations. The proposed framework uses a deep convolutional neural network (CNN), specifically a U-Net architecture with 3D operations, to map the composite microstructure to the corresponding stress and strain fields under a predetermined load path. In particular, the model is applied to a two-phase fiber reinforced plastic (FRP) composite microstructure subjected to a given loading-unloading path, predicting the corresponding stress and strain fields at discrete intermediate load steps. A novel two-step training approach provides more accurate predictions of stress, by first training the model to predict strain fields and then using those strain fields as input to the model that predicts the stress fields. This efficient data-driven approach enables accurate prediction of physical fields in inelastic materials, based solely on microstructure images and loading information.

Motivation & Objective

• To address the high computational cost of finite element method (FEM) simulations for predicting local inelastic responses in composite materials.
• To develop a data-driven surrogate model that accurately predicts micro-scale stress and strain fields under complex loading paths.
• To overcome limitations of prior ML models that only predict final-state fields or assume elastic behavior.
• To enable efficient, real-time prediction of evolving stress and strain fields during loading and unloading cycles in inelastic composites.
• To establish a framework that generalizes across different microstructures with arbitrary fiber arrangements, using only microstructure images and loading history.

Proposed method

• A 3D U-Net convolutional neural network is employed to perform image-to-image regression from microstructure images to full-field stress and strain tensor maps.
• The model is trained in a two-step process: first predicting strain fields from microstructure and load path, then using predicted strains as input to predict stress fields.
• The training data is generated via high-fidelity finite element simulations of two-phase FRP composites under a prescribed loading-unloading path.
• The network architecture leverages skip connections and 3D convolutions to preserve spatial resolution and capture hierarchical microstructural features.
• Loss functions are minimized using mean relative error (RE) between predicted and FEM-simulated fields to ensure high accuracy in local field prediction.
• Generalization is tested on unseen microstructures with random fiber arrangements, validating robustness across diverse configurations.

Experimental results

Research questions

• RQ1 Can a deep learning model accurately predict the evolution of local elasto-plastic strain and stress fields in a two-phase composite under a known loading-unloading path?
• RQ2 Does a two-step training strategy—first predicting strain, then using strain to predict stress—improve prediction accuracy compared to end-to-end training?
• RQ3 How does the model’s performance compare to finite element method (FEM) in terms of accuracy and computational speed for unseen microstructures?
• RQ4 To what extent can the model generalize to new microstructures with different fiber arrangements not seen during training?
• RQ5 What is the trade-off between training cost and inference speed when deploying such a model in multiscale or uncertainty quantification frameworks?

Key findings

• The model achieves a maximum mean relative error (RE) of approximately 1.1% for strain predictions on the loading path and 1.6% on the unloading path.
• For stress predictions, the maximum mean RE is 3.3% on the loading path and 5.9% on the unloading path, with median RE below 6% for unseen microstructures.
• The R² values for strain predictions range from 0.73 to 0.98, and for stress from 0.85 to 0.98, indicating strong agreement with FEM results.
• The predicted average stress-strain response closely matches the FEM simulation, confirming accurate macroscopic behavior reproduction.
• The model captures localized stress and strain concentrations with high fidelity, even in regions of plasticity and unloading.
• Inference time is reduced by several orders of magnitude compared to FEM, enabling rapid analysis for multiscale or uncertainty quantification applications.