Regularized Coulomb friction

1 · Separate normal pressure and tangential slip

First determine the compressive normal pressure from the declared contact route. In the tangent plane, measure relative slip since the last accepted state and form an elastic tangential trial force. The Coulomb limit is proportional to normal pressure, so friction capacity vanishes when the pair separates.

2 · Project the trial traction onto the friction bound

If the trial traction lies outside the admissible disk, return it to the boundary in the direction of the trial vector. This is the discrete stick/slip projection. The implementation's regularization and tolerances determine how transitions are smoothed near the switching surface.

3 · Assemble force, tangent, and state

Apply equal-and-opposite tangential forces to the two sides of the pair and add the route-specific tangential tangent to equilibrium. Persist the stick/slip state and accepted tangential history only after the global increment converges; otherwise restore the previous accepted state.

4 · Read the bounded claim correctly

Inspect pressure, tangential force, friction bound, stick/slip flag, and dissipation together. The documented case uses small transformations, a fixed initial projection and normal, a direct static solve, and stabilized translational DOFs. Mesh and regularization sensitivity remain material to the outcome.

This record does not establish general finite sliding, impact, self-contact, or frictional dynamics. Use the cited contract for the exact regularization parameter and acceptance thresholds.