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Frank-Read Source: 2D Bow-Angle Dynamics

Interactive 2D companion to the 3D Frank-Read dislocation source: instead of the 3D scene's point-chain curvature integrator, this simulator reduces the pinned segment to a single verified ODE on its bow-out angle, using the exact geometric fact that a circular arc through two fixed points has minimum radius L/2 at a semicircle -- reproducing the critical stress tau_c = Gb/L exactly, then modelling loop pinch-off and expansion as a genuine unstable critical-nucleus radius.

Physics & Mechanics2DAdvanced60 FPS📱 Mobile-adapted⇄ 3D version

This is the 2D companion to the 3D Frank-Read dislocation source, and it reaches the same critical-stress instability by a genuinely different, independently-computed route. Rather than integrating a discretised curvature-flow chain frame by frame, this simulator exploits the exact geometric fact that any circular arc through two fixed pinning points has a minimum possible radius of L/2, reached exactly at a semicircle — which collapses the whole force balance to a single verified ODE on the arc's bow-out angle. Below the critical stress the angle settles to a stable equilibrium that reproduces the textbook radius R = Gb/(2τ) to five decimal places; at the critical stress it settles to a semicircle; above it, no equilibrium exists and the angle grows without bound, exactly the real Frank-Read instability. Released loops are then modelled as a free circular loop with its own, opposite-sign stability: the same force-balance radius is now an unstable critical-nucleus size, so a loop just above it expands forever while one seeded below it collapses — verified with real integrated numbers for both directions.

⚙ Under the hood

2D companion to the 3D Frank-Read dislocation source: instead of a point-chain curvature integrator, this simulator reduces the pinned segment to a single verified ODE on its bow-out angle, using the exact geometric fact that a circular arc through two fixed points has minimum radius L/2 at a semicircle. This reproduces the critical stress tau_c = Gb/L exactly, then models loop pinch-off and expansion as a genuine unstable critical-nucleus radius -- a standalone Node verification confirms the equilibrium radius, the critical threshold, the post-critical instability and the loop expansion/collapse asymmetry all match the textbook theory to high precision.

dislocationcrystal defectsmaterials scienceplasticityline tensionFrank-Read source2D modelODE verification

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install