An incremental solution method for rough contact problems

J. A. Allwood

The numerical prediction of interfacial pressures in the mechanical contact of rough bodies has been studied widely. All published solution methods assume that the location of the region of contact between two approaching bodies is unknown and must be found by iterative trial and error. An alternative approach is presented in which the bodies are brought into contact incrementally. If the contact problem is described on a discrete grid and a valid solution is known for some applied load, it is possible to predict the location of the next point to enter contact and the increment in load required to cause this.

This incremental approach to solution is developed and a compact formulation is given. The method is compared with the fastest known existing solution method which also requires factorisation of the stiffness matrix and it is around six times slower. However having found the solution for a given load, the incremental approach has also found the complete loading history, so that the solution for any other load up to the given value is known without further calculation. In addition, solution for any higher load can begin from the existing solution.

This feature allows exploration of a variety of new applications: the history of body load against body displacement offers a simple means to determine characteristics of a surface texture; the impact of one rough body colliding with another is solved by the same incremental approach; problems with cyclic or dynamic loading can be studied without additional complexity; problems including both elastic and plastic deformation can be solved with improved convergence and allowing for work hardening during loading. While slower than other methods for solving static problems, the new incremental approach is inherently dynamic and thus more closely replicates the physical situations of concern to practical tribologists