PINN Stress Prediction for Notched Plates

ISEF Category: Engineering Technology: Statics and Dynamics

Subcategory: Computational Mechanics  ·  Difficulty: Advanced  ·  Setup: University Lab  ·  Time: Full Year

The Hook

A tiny notch can make a plate fail much sooner than you expect. That matters in airplane skins, bridges, and phone cases. You can model that weak spot with a neural network, then check if real light patterns match your math.

What Is It?

A physics-informed neural network, or PINN, is a machine learning model that does not just learn from examples. It also learns the physics rules that the answer must obey. In this case, those rules come from solid mechanics, the study of how materials carry force and bend, stretch, or crack.

Think of it like training a student who has to solve homework and show the work. The PINN does not only memorize stress maps from past shapes. It also tries to satisfy the equations that govern stress around notches, which are cutouts or missing pieces that concentrate force.

Photoelasticity gives you a visual check. When you place a stressed transparent plastic sample between polarized films, colored or dark fringe patterns appear. Those fringes act like contour lines on a map, and they reveal where stress builds up most strongly.

Why This Is a Good Topic

This is a strong science fair topic because you can change one shape, measure one output, and test one model against another. You can compare a PINN with finite element results and real fringe patterns, which gives you both computation and experiment in one project. The topic connects to real design problems in structures, vehicles, and consumer products, where stress concentration can cause cracks. You can learn geometry handling, model validation, image analysis, and error analysis.

Research Questions

• How does notch shape affect the peak stress predicted by a PINN?
• What is the effect of notch tip radius on the error between PINN and FEM stress maps?
• Does adding photoelastic fringe data improve PINN accuracy for irregular notch geometry?
• To what extent do symmetry assumptions change the PINN prediction near asymmetric notches?
• Which notch geometries produce the largest mismatch between photoelastic measurements and FEM results?
• How does training set size affect PINN error for stress concentration prediction?

Basic Materials

• Flat polycarbonate sheets for sample plates.
• Hobby knife or laser-cut access for making notches.
• Two linear polarized films.
• White LED light source.
• Digital camera or smartphone camera with manual exposure control.
• Clamps or a simple loading frame.
• Ruler or calipers.
• FreeCAD with CalculiX for comparison FEM models.
• Laptop for data processing and model training.
• ImageJ for fringe image measurements.

Advanced Materials

• Universal testing machine or custom tension frame.
• Photoelastic-grade polycarbonate samples.
• Circular polariscope components, including polarizer and analyzer films.
• Load cell with data acquisition.
• Strain gauge kit for spot checks.
• High-resolution camera with tripod.
• Finite element software, such as FreeCAD and CalculiX, or another validated solver.
• Python with PyTorch or TensorFlow for PINN training.
• GPU access for faster model training.
• Calibration weights or force standards.

Software & Tools

• Python: Runs the PINN model, data cleaning, and error analysis.
• PyTorch: Builds and trains the neural network with physics constraints.
• FreeCAD: Creates the notch geometries and prepares comparison models.
• CalculiX: Solves the finite element models for stress benchmarking.
• ImageJ: Measures fringe spacing and extracts image features from photoelastic photos.

Experiment Steps

1. Define the exact geometry family you want to study, such as one notch shape with one adjustable feature.
2. Choose the output you will predict, such as peak stress, stress concentration factor, or a full stress map.
3. Build a FEM baseline so you have a trusted numerical target for each geometry.
4. Plan the photoelastic setup and decide how you will turn fringe images into measurable data.
5. Design the PINN inputs, outputs, and physics loss terms so the model respects mechanics rules.
6. Set validation rules that compare all three sources, the PINN, FEM, and experiment, using the same geometry cases.

Common Pitfalls

• Training the PINN only on simple notch shapes, which makes it fail on irregular ones.
• Comparing fringe photos taken with different polarizer angles, which breaks image consistency.
• Using FEM outputs that do not match the exact boundary conditions of the physical sample.
• Measuring stress from blurry or overexposed fringe images, which hides the real peak pattern.
• Treating one geometry as enough proof, which makes the model look accurate without testing generalization.

What Makes This Competitive

A stronger project would test more than one notch family and report where the PINN succeeds and where it breaks. You would also get better results if you compare multiple loss functions, not just one training setup. Another strong move is to quantify uncertainty, then show how experimental noise changes the prediction error. That gives judges a clearer picture of whether the model is actually learning mechanics, not just memorizing shapes.

Project Variations

• Study circular, elliptical, and V-shaped notches to see which geometry creates the sharpest stress rise.
• Replace static loading with mixed loading directions and test whether the PINN still follows the same physics constraints.
• Compare grayscale fringe extraction with edge-based image features to see which data format helps model accuracy most.

Learn More

• MIT OpenCourseWare: Search for solid mechanics, finite element method, and machine learning for physical systems courses to build background on stress and modeling.
• NIST Chemistry WebBook and materials data pages are not the right fit here, so use the NIST site to search for measurement and uncertainty resources instead.
• NASA Technical Reports Server: Search for photoelasticity, structural analysis, and machine learning papers that use physics-based modeling.
• PubMed: Search review articles on physics-informed neural networks and inverse problems for methods and validation ideas.
• Journal of Strain Analysis for Engineering Design: Search recent papers on photoelasticity, stress concentration, and notch analysis.
• USGS Publications Warehouse: Search for general finite element and fracture mechanics reports if you want examples of validated stress analysis workflows.