Analytical frequency response functions for contact of multilayered materials

• We derived the analytical solutions for multilayered materials.
• We built a contact model for multilayered materials using the derived solutions.
• Contacts involving materials with various numbers of layers were investigated.

Multilayer coatings are often seen in surface engineering for surface modifications. Optimal design of the multilayered materials requires the understanding of their mechanical behaviors based on deformation and stress analyses. The frequency response functions (FRFs) of the displacement and stress fields in multilayered materials under unit normal and shear loadings are the analytical cores for solving the contact of such materials. The authors have successfully derived these functions by utilizing the Papkovich–Neuber potentials and appropriate boundary conditions. Two matrix equations containing unknown coefficients in the FRFs are established by following the structure rules, and then the closed-form FRFs written in a recurrence format are established. A fast numerical semi-analytical model based on the derived FRFs is further developed for investigating the elastic contact of multilayered materials with any desired material design.