Analytical frequency response functions for contact of multilayered materials

Chengjiao Yu, Zhanjiang Wang*, Q. Jane Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)102-120
Number of pages19
JournalMechanics of Materials
StatePublished - Sep 2014


  • Analytical frequency response functions
  • Coatings
  • Contact modeling
  • Multilayered materials

ASJC Scopus subject areas

  • Materials Science(all)
  • Instrumentation
  • Mechanics of Materials


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