Modeling of Contact Interaction of Two-Layer Bodies Taking into Account Adhesion and Rheological Properties of Coating or Substrate Materials

A numerical-analytical method is proposed for calculating contact pressures and internal stresses that arise in a two-layer elastic half-space when a smooth indenter of arbitrary shape is indented, taking into account adhesion forces. The Maugis-Dugdale adhesion interaction model is used. The influence of layer thickness and the presence of adhesive attraction on the penetration of the indenter, as well as on internal stresses, was analyzed. The simulation results can be used to solve the inverse problem – determining the elastic modulus of the coating based on the results of indentation, taking into account adhesion and deformation of the substrate. The sliding of a smooth indenter along the boundary of a two-layer half-space is considered, taking into account the rheological properties of materials. The case of a viscoelastic layer associated with a rigid half-space is analyzed, as well as the opposite case – a viscoelastic half-space covered with a rigid layer. The problem is formulated as quasi-static. The numerical-analytical solution method is based on the boundary element method and an iterative procedure. An analytical relationship for calculating influence coefficients is obtained. Contact pressure, energy dissipation and internal stresses are analyzed as a function of sliding speed, layer thickness and Poisson’s ratio.