Time-discretized Variational Formulation of Nonsmooth Frictional Contact

Pandolfi, A., C. Kane, J. E. Marsden and M. Ortiz

Int. J. Num. Methods in Engineering 53, 1801-1829.

Abstract:

The present work extends the nonsmooth contact class of algorithms introduced by Kane, Repetto, Ortiz and Marsden in 1999 to the case of friction. The formulation specifically addresses contact geometries, e. g., involving multiple collisions between tightly packed nonsmooth 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.