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 beneÞt 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. E¤ectiveness of the algorithm is demonstrated by a series of Þnite element simulations involving large deformations and frictional slip, complete with appropriate comparisons to more traditional schemes