A thermodynamically consistent phase-field framework for viscoelastic fatigue fracture with dissipated-energy-driven toughness degradation

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For implementers, the locking model adds a fair amount of non-trivial internal bookkeeping. Every operation must check lock state, readers must be tracked, and the interplay between locks, cancellation, and error states creates a matrix of edge cases that must all be handled correctly.

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To find these crucial border points, we employed a clever technique based on the Ford-Fulkerson algorithm. By simulating "flooding" roads with traffic from random start/end points, we could identify the natural bottlenecks – the "minimum cut" in graph theory terms. These bottlenecks became our border points.