LIVE93.4% IMPROVEMENT

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

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The Physics

In fracture mechanics, the stress field near a crack tip follows:

sigma = K / sqrt(2*pi*r)

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/dr[1/sqrt(r)] = -1/(2*r^1.5) (diverges)
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 →