Flat Rolling Friction Hill: Roll-Bite Pressure Distribution (2D)

This 2D companion to the 3D flat-rolling mill simulator replaces the single closed-form force estimate with the real slab-method calculation used in rolling-mechanics theory: the friction-hill differential equation is integrated numerically along the contact arc from both the entry and exit boundaries, with Coulomb friction capped at the shear-yield "sticking" limit near the peak. The point where the two solutions meet is the neutral (no-slip) point, found directly from the physics rather than from a small-angle approximation. Watch the pressure curve build from the flow stress at each edge up to a peak at the neutral point, compare the resulting roll-separating force against the 3D twin's closed-form estimate, and see the same mass-conservation strip-speed profile driven by the corrected neutral-point location.