Plastic deformation of a sinusoidal surface

Simple upper bound plastic mechanisms are developed to relate the pressure and contact area for a partially flattened sinusoidal profile. The resulting surface deformation is calculated, and the results are compared with the elasto-plastic simulation results of Gao, Bower, Lev and Cheng. A lower bound stress field solution is also developed to show that the assumption of rigid-perfectly plastic behaviour tends to infinite pressure as the surface tends towards complete contact. Hence the finite limiting pressures found by Gao et al must be the result of an elastic–plastic interaction.