Patrick Kane vs. Hayley Pandolfi

In the sports world, Patrick Kane and Hayley Pandolfi are battling head-to-head in a he-said/she-said story of their sexual encounter.

But in the world of science, the two are reunited. Time-discretized variational formulation of non-smooth frictional contact was a 2001 article in the International Journal for Numerical Methods in Engineering and was authored by Anna Pandolfi and Couro Kane (along with fellow CalTech grad students Jerrold E. Marsden and Michael Ortiz).
The present work extends the non-smooth contact class of algorithms introduced by Kane et al. to the case of friction. The formulation specifically addresses contact geometries, e.g. involving multiple collisions between tightly packed non-smooth bodies, for which neither normals nor gap functions can be properly defined. A key aspect of the approach is that the incremental displacements follow from a minimum principle. The objective function comprises terms which account for inertia, strain energy, contact, friction and external forcing. The Euler–Lagrange equations corresponding to this extended variational principle are shown to be consistent with the equations of motion of solids in frictional contact. In addition to its value as a basis for formulating numerical algorithms, the variational framework offers theoretical advantages as regards the selection of trajectories in cases of non-uniqueness. We present numerical and analytical examples which demonstrate the good momentum and energy conservation characteristics of the numerical algorithms, as well as the ability of the approach to account for stick and slip conditions.

The "he said", as so very often happens, looks to be correct. This past week Hayley Pandolfi stopped cooperating with investigators and the prosecutor announced that Kane will never face a Grand Jury because the physical evidence backed his side of the story.