Time-discretized variational formulation of non-smooth frictional contact
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.
© 2001 John Wiley & Sons, Ltd. Received 4 September 2000. Revised 18 January 2001. Article first published online: 27 Dec. 2001. Contract/grant sponsor: AFOSR, partially; contract/grant number: F49620-96-1-0471. Contract/grant sponsor: DoE, partially. Contract/grant sponsor: Army Research Office; contract/grant number: DAAH04-96-1-0056. CK, JEM and MO are grateful to the AFOSR for partial support through Caltech's MURI on Mathematical Infrastructure for Robust Virtual Engineering. MO is grateful to the DoE for partial support through Caltech's ASCI Center for the Simulation of the Dynamic Response of Materials. MO also wishes to gratefully acknowledge the support of the Army Research Office through grant DAAH04-96-1-0056. AP gratefully acknowledges helpful discussions with Dr Antonella Abbá of the Department of Mathematics of the Politecnico di Milano.