Energy consistent algorithms for frictional contact problems

In this paper, the energy and momentum conserving algorithmic paradigm is extended to encompass a phenomenon featuring physical dissipation: dynamic frictional contact. Whereas in other works dealing with conservative systems the chief aim is often the maintenance of numerical stability in the non-linear regime, in this investigation we seek to achieve not only this benefit but also the accurate algorithmic production of physical dissipation associated with frictional processes. The approach here features a product formula algorithm for the evolution of local frictional conditions, with the associated operator split guided by an a priori energy estimate. The resulting algorithm is characterized by exact conservation of energy during stick friction, and positive dissipation consistent with the frictional model used during slip. Effectiveness of the algorithm is demonstrated by a series of finite element simulations involving large deformations and frictional slip, complete with appropriate comparisons to more traditional schemes. © 1998 John Wiley & Sons, Ltd.