14. Contact Mechanics in the Framework of Couple Stress Elasticity

The purpose of this work is to present general solutions for two-dimensional (2D) plane-strain contact problems within the framework of the generalized continuum theory of couple-stress elasticity. This theory is able to capture the scale effects, which are often observed in indentation problems with contact lengths comparable to the material microstructure. To this end, we formulate a number of basic contact problems in terms of singular integral equations using the pertinent Green’s function that corresponds to the solution of the analogue of the Flamant-Boussinesq problem of a half-space in couple-stress elasticity. In addition, we also provide results concerning the more complex traction boundary-value problem involving a deformable layer (again within couple-stress elasticity) of finite thickness superposed on a rigid half-space. We show that the contact behavior of materials with couple-stress effects depends strongly upon their microstructural characteristics, especially when the characteristic dimension of the microstructure becomes comparable to macroscopic characteristic dimensions of the contact problem. The latter lengths could be either the contact length/area or even the thickness of the layer.