StampFormer: A Physics-Guided Material-Geometry-Coupled Multimodal Model for Rapid Prediction of Physical Fields in Sheet Metal Stamping

Technical Summary: StampFormer

Problem Statement
Traditional sheet metal forming design relies on Finite Element Analysis (FEA) for validation. While FEA provides high-fidelity predictions of physical fields (e.g., thinning, strain, displacement), it is computationally expensive, often requiring hours to days per simulation. This latency creates a bottleneck in the design cycle, preventing rapid iteration and real-time manufacturability assessment. Existing AI-based surrogate models attempt to accelerate this process but suffer from significant limitations: scalar-based models fail to capture comprehensive spatial field information, while current image-based models typically focus solely on part geometry, neglecting the critical influence of material properties (stress-strain responses) on forming outcomes.

Methodology
To address these gaps, the authors propose StampFormer, a physics-guided, material-geometry-coupled multimodal deep learning framework. The model is designed to accept two distinct input modalities:

1. Geometric Data: A 2D height-map image (608 × 768 pixels) derived from 3D CAD geometries via Z-plane projection.
2. Material Data: A 1D vector representing the stress-strain curve (sampled at 100 points).

The architecture consists of three core components:

• Material-Augmented Geometric Network (MAGN): This module performs the initial fusion of modalities. It processes the 1D stress-strain curve through a Transformer Encoder to generate a global material embedding. This embedding is then mapped into the spatial domain via a Multi-Layer Perceptron (MLP) and added to the geometric feature map (Material-Aware Feature Modulation). The raw geometry is concatenated with this fused feature map to preserve boundary information before being passed to the backbone.
• Hierarchical Material Embedding Injection Unit (HMEIU): To ensure material properties influence the network at all scales, this unit operates in parallel with the encoder. It refines the material embeddings at multiple hierarchical levels and injects them into the main data stream after each downsampling (Patch Merging) stage. This allows the model to learn how global material characteristics affect both fine-grained and abstract geometric features.
• Physics-Guided Swin-UNet (PGSU): The backbone is an adapted Swin-UNet, utilizing Window-based Multi-head Self-Attention (W-MSA) within a symmetric encoder-decoder structure. It processes the material-augmented features to predict the final physical fields.

Data Generation
The study utilized two datasets: one for steel and one for aluminium.

• Material Data: Virtual material datasets were generated to ensure diversity. The steel dataset was expanded from 101 real curves to 600 augmented curves across five clusters. The aluminium dataset was expanded from 11 real curves to 110 augmented curves.
• Geometric Data: 600 unique 3D CAD geometries were generated using Latin Hypercube Sampling (LHS) across key parameters (radii, draft angles, bead dimensions).
• Simulation: A total of 6,000 FEA simulations (3,000 per material) were run using PAM-STAMP. Each simulation paired a unique geometry with a material from a specific cluster. The 3D FEA results were mapped back to the initial 2D blank to create target images for thinning, major strain, minor strain, plastic strain, and 3D displacement.

Key Contributions

1. Multimodal Integration: StampFormer is presented as one of the first image-based sheet-forming surrogates to explicitly combine 2D part geometry with 1D material stress-strain responses, addressing the limitation of geometry-only models.
2. Dual-Stage Fusion Strategy: The introduction of MAGN and HMEIU enables effective cross-modal fusion, ensuring material properties are integrated at both the initial input level and throughout the hierarchical feature extraction process.
3. Comprehensive Field Prediction: Unlike scalar-based surrogates, the model predicts full-field results for five critical physical outputs (thinning, major/minor/plastic strain, and displacement) rather than single scalar metrics.

Results
The model was evaluated on a test set comprising 300 samples for each material (steel and aluminium).

• Accuracy: The model achieved an average relative error of less than 8.5% for the four 2D physical fields (thinning, strains). For the 3D displacement field, the Mean Squared Error (MSE) was less than 1.2 mm².
• Specific Performance:
  • Steel: Mean relative errors ranged from 4.5% to 7.2% across the 2D fields.
  • Aluminium: Mean relative errors ranged from 3.5% to 8.2%. The authors note slightly higher error tails for aluminium, attributing this to its lower ductility and sharper strain gradients.
• Visual Agreement: Qualitative analysis of Forming Limit Diagrams (FLDs), thinning maps, and reconstructed 3D surfaces showed strong agreement with ground truth FEA results, particularly in identifying critical thinning regions and part shapes.
• Speed: While FEA simulations required several hours, StampFormer provided predictions in under one second on a single GPU, representing a speed-up of over three orders of magnitude.

Significance
The authors claim that StampFormer offers a practical and efficient framework for real-time manufacturability assessment early in the design cycle. By integrating material properties with geometry, the model enables designers to perform rapid feasibility checks that were previously impossible due to FEA latency. The framework supports a shift from traditional, linear design-validation workflows to an AI-empowered, interactive process. The study emphasizes that the model's ability to generalize across a broad range of material properties and geometric variations makes it suitable for industrial screening, though the authors note that transferability to entirely new part families remains a direction for future work.