Organizations: Tech Hive Labs, Iliados 7, Halandri, 152 32, Greece. · Université Marie et Louis Pasteur, SUPMICROTECH, CNRS, Institut FEMTO-ST, Besançon, F-25000, France. · AI Innovation Centre, University of Essex, Little Abington, Cambridge, CB21 6AL, UK.
Plant fibers are increasingly used as sustainable reinforcements in composites, but the intrinsic variability of their microstructure causes substantial scatter in transverse mechanical behavior, complicating composite design. Characterizing this behavior relies on finite element (FE) simulations requiring several minutes of high-performance computing per fiber, making high-throughput characterization across realistic fiber populations impractical. In this study, we propose a deep learning framework replacing this FE bottleneck with a fast pipeline. It includes two coupled recursive U-Nets predicting the step-by-step evolution of fiber deformation and internal stress fields under transverse compression, followed by a regression CNN estimating the transverse Young's modulus from the final stress field. Unlike prior approaches predicting stress fields for fixed configurations or idealized geometries, our framework recursively resolves the full temporal stress evolution for synthetic fibers derived from real hemp cross-sections, with or without a lumen. Trained on 1,000 synthetic fiber geometries with FE ground truth, it reproduces the stress field sequence with a Structural Similarity Index Measure (SSIM) of 0.9574±0.0074 and a Root Mean Squared Error (RMSE) of 0.0345±0.0079. It estimates transverse Young's modulus with an R2 of 0.938±0.024, a Mean Absolute Error (MAE) of 24.31±1.23 MPa, and a Mean Absolute Percentage Error (MAPE) of 5.25±0.91%. Inference requires under one second per fiber versus five minutes per FE simulation, drastically reducing computational cost. This offers a fast, reliable tool for mechanical characterization of synthetic plant fibers, with promising applications in designing natural fiber-reinforced composites.
Figures & tables
Figure 1: Extracted and smoothed hemp fiber cross-sectional geometries used for finite element analysis, showing examples of fibers with and without lumen. Reprinted from Composites Part A: Applied Science and Manufacturing, Vol 175, Jason Govilas, Cédric Clévy, Johnny Beaugrand, Vincent Placet, Investigating the influence of plant fiber geometry on apparent transverse elastic properties through finite element analysis, 107789, Copyright (2023), with permission from Elsevier Govilas et al. (2023) .
Figure 2: The progressive evolution of the internal stress field output from the FE transverse compression simulations at selected loading intervals.
Figure 3: The pre-processing steps applied to the FE output sequences.
Figure 4: Schematic representation of the deep learning pipeline. Starting from the initial fiber mask, the Deformation U-Net predicts the evolving fiber geometry step by step. At each step, the Stress U-Net predicts the corresponding physical stress field, conditioned on the predicted deformation. The final predicted stress field is then passed to the Modulus CNN, which estimates the transverse Young’s modulus ( ET ).
Hyperparameter
Regression
Image-to-Image
Input size
(256,256)
(256,256)
Number of layers
4
4
Number of initial filters
64
32
Convolution kernel
3×3
3×3
Pooling size
4
2
Bottleneck dimension
32
128
Table 1: Hyperparameters of the deep learning models
Figure 5: The ET distribution of the training-evaluation split with different experiment seeds.
Model
SSIM (0–1) ↑
RMSE (0–1) ↓
Stress U-Net (ours)
0.9574 ± 0.0074
0.0345 ± 0.0079
StressNet Nie et al. (2019)
0.9372 ± 0.0048
0.0438 ± 0.0022
StressNet-mod Shokrollahi et al. (2023) ; Sun et al. (2024)
0.9172 ± 0.0240
0.0479 ± 0.0094
U-Net-mod Bhaduri et al. (2022)
0.9170 ± 0.0218
0.0563 ± 0.0090
SCSNet Nie et al. (2019)
0.8076 ± 0.0290
0.0894 ± 0.0023
Table 2: Comparative evaluation of stress field prediction models
Figure 6: Qualitative evaluation of the proposed framework for stress field prediction of individual synthetic plant fibers under transverse compression.
Model
R 2 (0–1) ↑
MAE (MPa) ↓
MAPE (%) ↓
Modulus CNN (ours)
0.938 ± 0.024
24.31 ± 1.23
5.25 ± 0.91
ResNet-34 He et al. (2015)
0.895 ± 0.059
30.48 ± 6.84
6.89 ± 1.70
AlexNet Krizhevsky et al. (2012)
0.881 ± 0.088
28.42 ± 3.91
6.67 ± 0.49
TI-CNN Wang et al. (2021)
0.837 ± 0.079
35.94 ± 7.07
8.10 ± 0.98
CNN-custom Raaghav et al. (2025)
0.754 ± 0.014
48.04 ± 8.89
10.49 ± 2.11
Table 3: Comparative evaluation of regression models for transverse Young’s modulus prediction
Group
n
MAPE (%)
Bias (%)
MAE (MPa)
R 2
Overall
70
5.25±0.91
−0.60±1.70
24.31±1.23
0.938±0.024
Low-modulus ( ET≤ median)
35
5.52±2.14
+0.15±2.26
19.28±4.82
0.917±0.033
High-modulus ( ET> median)
35
5.04±0.36
−1.66±2.01
29.93±4.38
0.595±0.297
Table 4: Prediction performance of the Modulus CNN, stratified by true modulus, averaged over 3 seeds ( ± std across seeds). Groups are split at the pooled median true ET . n is the number of held-out test samples per group, pooled over the 3 seeds.
Group
n
MAPE (%)
Bias (%)
MAE (MPa)
R 2
Overall
70
5.25±0.91
−0.60±1.70
24.31±1.23
0.938±0.024
No lumen
46
5.11±0.11
−0.59±1.53
28.09±2.40
0.797±0.104
With lumen
24
5.24±2.60
−0.88±3.03
16.48±6.61
0.930±0.038
Table 5: Prediction performance of the Modulus CNN, stratified by lumen presence, averaged over 3 seeds ( ± std across seeds). n is the number of held-out test samples per group, pooled over the 3 seeds.
Model
Target
SSIM (0–1) ↑
RMSE (0–1) ↓
Full
Deformation
0.9822 ± 0.0015
0.0761 ± 0.0037
Stride-1
Deformation
0.9805±0.0024
0.0820±0.0053
Full
Stress
0.9574 ± 0.0074
0.0345 ± 0.0079
Stride-1
Stress
0.8923±0.0083
0.0734±0.0102
No-def
Stress
0.8235±0.0290
0.0903±0.0137
No-rec
Stress
0.5162±0.0316
0.1333±0.0014
Table 6: Ablation study of the image-to-image model
Figure 7: Qualitative comparison of rollout predictions for stride values Δ=1 and Δ=4 across sequential evaluation steps.
Short-fiber thermoplastic (SFT) composites are increasingly employed in lightweight aerospace and automotive structures owing to their favorable strength-to-weight ratio, high production rates, and recyclability. Unlike continuous-fiber systems, the mechanical response of SFTs is governed by mesoscale interactions among fiber orientation, spatial clustering, and manufacturing-induced porosity. These features exhibit significant spatial variability in manufactured components and influence stiffness, damage initiation, and nonlinear deformation. Although mesoscale finite element (FE) models can resolve such heterogeneity, their application to realistic three-dimensional microstructures remains computationally intractable. A data-driven surrogate framework is proposed to predict the mechanical behavior of additively manufactured, compression-molded (AM-CM) SFTs. Microstructures reconstructed from micro-computed tomography data were discretized into Voronoi-based cells representing distinct fiber-interaction neighborhoods. Each cell was homogenized via nonlinear FE simulations incorporating matrix damage, and the resulting stress-strain responses trained a hybrid Graph Neural Network-Long Short-Term Memory (GNN-LSTM) architecture encoding microstructural topology and history-dependent mechanical evolution. The surrogate accurately predicts stiffness and stress-strain behavior of unseen microstructures, achieving R2≈0.98 relative to high-fidelity FE simulations with over two orders-of-magnitude reduction in computational cost. Coupling the framework with experimentally calibrated damage laws demonstrates that fiber orientation, clustering, and porosity collectively govern local effective stiffness. The approach provides a physics-informed, data-efficient pathway to identify mechanically weak microstructural cells and accelerate digital-twin development for SFT components.
Pharindra Pathak, Vipin Kumar, Trenton M. Ricks +2
Auburn University, Oakridge National Lab, NASA Glenn Research Center, Auburn University, Auburn University · Graduate Student, Department of Aerospace Engineering, Auburn University, Auburn, AL · Sr. R&D Staff Member, Manufacturing Science Division, ORNL, Knoxville, TN +3
Finite Element Analysis (FEA) is widely used for transient mechanical simulations, but its high computational cost limits real-time and high-resolution applications. Deep learning surrogate models can reduce this cost; however, many existing approaches are restricted to steady-state prediction or cannot jointly predict Node- and Element-based Outputs (NEO) over time. The state-of-the-art DeepFEA framework has addressed these issues but remains limited to structured finite element (FE) meshes. To overcome this limitation, this study proposes DeepFEAv2, a deep learning surrogate framework that enables prediction of transient FEA simulations across different FE mesh topologies and element types. The main contributions of DeepFEAv2 are: (a) a module that uses the FE connectivity matrix to organize input features by element and arrange them into an input sequence guided by the mesh topology; (b) a novel neural network architecture designed to process the input sequence and jointly predict NEO over time; and (c) a FEA-informed optimization strategy for regularizing these NEO predictions. DeepFEAv2 was evaluated on structured and unstructured 3D linear elastic datasets, as well as on a pressure-driven aortic valve dataset. DeepFEAv2 achieved R^2 values up to 0.99 and normalized errors as low as 0.38%. Compared with DeepFEA, it achieved up to 38.0% relative increase in R^2 and up to 87.1% reduction in normalized error. DeepFEAv2 also performed inference up to three orders of magnitude faster than traditional FEA. These results demonstrate that DeepFEAv2 can efficiently model transient FEA simulations across increasingly complex FE settings, providing a scalable surrogate framework for transient FEA.
Georgios Triantafyllou, Panagiotis G. Kalozoumis, Dimitris K. Iakovidis
Department of Computer Science and Biomedical Informatics, University of Thessaly, 2-4 Papasiopoulou st. 35131, Lamia, Greece
Accurate prediction of stress and strain fields in hierarchical composite microstructures is critical for physics-informed material design, yet conventional finite element method (FEM) simulations are computationally prohibitive at scale, requiring minutes to days per evaluation. In this work, we propose a hybrid UNet-Transformer architecture that predicts complex mechanical field distributions directly from composite microstructure geometry images, serving as an efficient surrogate for FEM across ten distinct stress and strain field types spanning diverse two-phase composite configurations including square, hexagonal, and triangular tessellations, multiple boundary conditions, and high-resolution geometries. Results demonstrate that the proposed architecture achieves strong predictive performance across the majority of subdatasets, with peak accuracy on periodic tessellation geometries reaching R2=0.9991, SSIM=0.9936, and MAE=0.0050 on the boundary condition subdataset and the triangular tessellation subdataset respectively. Across six of the eight evaluated subdatasets, MAE remains below 0.05 on the normalized [0,1] pixel scale. Encoder attention analysis via Grad-CAM and Grad-CAM++ confirms that the model develops physically meaningful internal representations, localizing attention at mechanically critical regions including phase boundaries, ligament junctions, and indenter contact zones without explicit structural supervision. Performance degrades on irregular square-grid geometries with sparse soft-phase inclusions, with the S11 normal stress subdataset yielding R2=0.7735 and SSIM=0.7126, consistent with the known limitation of smooth-loss image translation models in reproducing sharp stress discontinuities.
Shrey Patel
University of Maryland-College Park United States of America