Semi-analytical solution of three-dimensional steady state thermoelastic contact problem of multilayered material under friction heating

Multilayer coatings offer a possibility to design the surface according to the different requirements, which attracts intense attentions from engineering and research community. The coupled thermo-mechanical contact problem of a multilayered material is of great interest. This paper firstly derives the frequency response functions (FRF) of thermoelastic fields through thermoelastic governing equations. The unknown coefficients in the FRFs are assembled in a linear system of matrix equations according to the thermal and mechanical loadings on surface and continuity condition of heat flux, temperature, displacement and stresses at each interface; then the coefficients are solved and expressed recursively. Based on the closed-form solution of FRFs, a fast semi-analytical method (SAM) is developed to solve the three-dimensional thermoelastic contact problem involved in arbitrary multilayered materials. There are no limits on the number or the thickness of layers, and material parameters can be varied arbitrarily. The present model is verified by literature and FEM and shows a high robustness and efficiency. Thermoelastic contact of multilayered materials with different coating designs under friction heating is further studied and the thermal effect is explored.