A numerical three-dimensional model for the contact of layered elastic/plastic solids with rough surfaces by a variational principle

A new numerical model for the three-dimensional contact analysis of a layered elastic-perfectly plastic half space with another rough surface is presented. The model is based on a variational principle in which the real area of contact and contact pressure distribution are those which minimize the total complementary potential energy. A quasi-Newton method is used to find the minimum. The influence coefficients matrix is determined using the Papkovich-Neuber potentials with fast Fourier transformation. The model is extended to elastic-perfectly plastic contacts in dry and wet conditions. Contact analyses have been performed to predict contact statistics of layered elastic/plastic solids with rough surfaces using this model. The effects of the stiffness of the layer and the substrate, laver thickness, as well as normal load are studied. Optimum layer parameters are identified to provide low friction/stiction and wear.