Source-linked AI summary
Stress field prediction in fiber-reinforced composite materials using a deep learning approach
Anindya Bhaduri, Ashwini Gupta, Lori Graham-Brady
TL;DR
FEM-based stress analysis can be costly for complex geometries, motivating machine-learning alternatives. This study uses U-Net models to predict von Mises stress fields in fiber-reinforced composites, including transfer learning from cheaper, smaller-fiber systems; results generally improve with more data, and pretrained models are superior in almost all evaluated cases.
Problem
FEM stress analysis can be costly for complex geometries, while increasing fiber counts at fixed volume fraction requires finer meshes and greater computational cost.
Method
U-Net models are trained on plane strain FEM data to map arbitrary fiber arrangements to von Mises stress fields, with sensitivity analysis and transfer learning across fiber counts.
Results
U-Net accurately predicts von Mises stress fields for 6-, 10-, 20-, and 100-fiber plates, while prediction accuracy improves with increased training data and pretrained models are superior in almost all evaluated transfer-learning cases.
Takeaways & Limitations
The study demonstrates a deep-learning alternative for stress-field prediction and supports using information from smaller-fiber systems to reduce training effort for larger-fiber systems in many cases.
Takeaways & Limitations
Transfer learning from 6-fiber data can be ineffective for 50-fiber systems because their stress distributions differ substantially.
Abstract
from arXiv · showhide
Computational stress analysis is an important step in the design of material systems. Finite element method (FEM) is a standard approach of performing stress analysis of complex material systems. A way to accelerate stress analysis is to replace FEM with a data-driven machine learning based stress analysis approach. In this study, we consider a fiber-reinforced matrix composite material system and we use deep learning tools to find an alternative to the FEM approach for stress field prediction. We first try to predict stress field maps for composite material systems of fixed number of fibers with varying spatial configurations. Specifically, we try to find a mapping between the spatial arrangement of the fibers in the composite material and the corresponding von Mises stress field. This is achieved by using a convolutional neural network (CNN), specifically a U-Net architecture, using true stress maps of systems with same number of fibers as training data. U-Net is a encoder-decoder network which in this study takes in the composite material image as an input and outputs the stress field image which is of the same size as the input image. We perform a robustness analysis by taking different initializations of the training samples to find the sensitivity of the prediction accuracy to the small number of training samples. When the number of fibers in the composite material system is increased for the same volume fraction, a finer finite element mesh discretization is required to represent the geometry accurately. This leads to an increase in the computational cost. Thus, the secondary goal here is to predict the stress field for systems with larger number of fibers with varying spatial configurations using information from the true stress maps of relatively cheaper systems of smaller fiber number.
1. Introduction
The study frames deep learning as a potential surrogate for costly FEM stress analysis and targets local stress prediction in fiber-reinforced composites. It pursues fixed-fiber prediction, robustness to small training sets, and transfer to larger-fiber systems.
- FEM is conventional for stress analysis but can be costly for nonlinear problems, complex geometries, and multiscale analyses.
- Deep learning has been applied to predict von Mises stress fields in two-dimensional solid and composite structures.
- The primary goal is predicting an N-fiber plate’s stress field from arbitrary spatial fiber arrangements using plane-strain FEM training data.
- A sensitivity analysis evaluates prediction robustness when training datasets are small.
- The secondary goal is predicting M-fiber systems from cheaper N-fiber training data when M > N.
2. Methodology
The methodology represents composite microstructures and FEM stress fields as paired images, then learns their mapping with an encoder-decoder U-Net. The setup uses simplified plane-strain composite models with fixed circular fibers and prescribed tensile loading.
- 2.1. Problem setup: The problem uses a two-dimensional plane-strain composite cross-section with linear-elastic fibers and matrix.
- 2.1. Problem setup: Circular fibers have fixed radius, constant volume fraction, and perfectly bonded fiber/matrix interfaces.
- 2.1. Problem setup: Horizontal tensile strain is applied with traction-free top and bottom boundaries, producing a von Mises stress field.
- 2.2. Approach overview: FEM simulations generate paired input microstructure images and output stress-map images for training.
- 2.3. U-Net architecture: The binary fiber/matrix image is encoded into a latent space and decoded into a stress field using a U-Net mapping.
- 2.3. U-Net architecture: U-Net combines contracting and expanding layers with skip connections that propagate context and enhance output resolution.
3. Results
The U-Net predicted von Mises stress maps for composite systems with 6, 10, 20, and 100 fibers from limited FEM-generated training data. Prediction accuracy improved with larger training sets, while transfer learning helped mainly when target systems had limited data.
- 3.1. Stress map prediction accuracy: 25 FEM simulations per system were augmented through horizontal, vertical, and combined horizontal–vertical image flips.The augmentation produced 100 training images for the evaluated composite systems.
- 3.1. Stress map prediction accuracy: U-Net predictions for 6-, 10-, 20-, and 100-fiber systems showed relatively small stress-map errors compared with the FEM maps.The reported comparisons use true FEM von Mises stress maps, predicted maps, and corresponding stress-error maps.
- 3.2. Effect of training size on stress map accuracy: Four metrics assessed robustness across 20 training runs with different random-seed initializations and training datasets.The metrics were weighted MSE, mean maximum error, median maximum error, and normalized RMSE.
- 3.2. Effect of training size on stress map accuracy: Increasing training-data size increased mean accuracy and decreased its variance across the evaluated composite systems.Figures 10–13 report metric convergence for the 6-, 10-, 20-, and 100-fiber systems.
- 3.2. Effect of training size on stress map accuracy: Overall error across all metrics decreased as fiber number increased from 6 to 100, attributed to high stresses becoming localized over smaller regions.The stress-field magnitudes were reported as similar across the different composite systems.
- 3.3. Deep transfer learning: Transfer learning from a 6-fiber model improved 20-fiber prediction over training from scratch, especially when using limited target-system data.For 50-fiber systems, the advantage was observed at smaller training sizes but diminished with larger datasets; with 100 target samples, pretraining could be worse than training from scratch.
4. Conclusions
The study uses U-Net models to predict von Mises stress fields for composite plates with varying fiber counts and arrangements, while assessing training-data sensitivity and transfer learning. The authors report improved accuracy with more data and generally better pretrained performance for higher-fiber systems.
- U-Net predicts von Mises stress fields for 6-, 10-, 20-, and 100-fiber composite plates with arbitrary fiber arrangements under uniaxial tension.
- Prediction accuracy improves as the training dataset grows, based on a sensitivity analysis using different training-data sizes.
- Transfer learning uses a U-Net pretrained on 6-fiber data to predict stress distributions in 20- and 50-fiber systems.
- In almost all cases, the pretrained network achieves superior accuracy for the higher-fiber systems.
- Future extensions include predicting all stress components for arbitrary strain vectors and modeling interfacial debonding, constituent damage, and time-dependent damage evolution.