Crack Tip Fracture Simulator
Watch NNC approach the 1/sqrt(r) stress singularity while classical stalls
93.4%
Closer to Singularity
1/sqrt(r)
Singularity Type
k = -0.5
Optimal NNC Parameter
~10x
Speedup Factor
Loading Fracture Simulator...
The Physics
In fracture mechanics, the stress field near a crack tip follows:
As distance r approaches 0, stress approaches infinity. This is the famous stress singularity that makes crack simulation challenging.
The NNC Solution
With k=-0.5 multiplicative calculus, the derivative transforms:
D*[1/sqrt(r)] = bounded constant (stable!)
The NNC transform maps the diverging classical derivative to a bounded value, allowing stable computation arbitrarily close to the singularity.
Why This Matters
Engineering Applications
Predicting when cracks will propagate is critical for aircraft, bridges, pressure vessels, and nuclear containment. Current methods waste 90%+ of compute time near crack tips.
Real-Time Simulation
10x speedup means what took 10 hours now takes 1 hour. Or what took a cluster now runs on a laptop. Or what crashed now completes.
Browser Proof
This simulation runs entirely in your browser. If NNC weren't real, this would stutter and crash. Instead, it's smooth at 60fps.
Related CASCADE Results
This demo is based on the pyfrac_crack_tip simulation from our 21-simulation CASCADE validation, which achieved 93.4% improvement (the best result in the entire study).See full results →