Methods for analysing partial contact between surfaces

This paper reviews methods available for the numerical solution of contact mechanics problems, in particular, those in which the extent of the contact(s) is not known at the start of the analysis. A new objective function is proposed which is generally smooth and which enables contact mechanics problems to be solved by unconstrained minimisation, in spite of the non-linear boundary condition at the interface. The application of the method to plane periodic elastic contacts, and the authorʹs previously published M(x) formulation of such cases, is demonstrated in detail.