On the contact and adhesion of a piezoelectric half-space under a rigid punch with an axisymmetric power-law profile

Abstract

The present paper provides a theoretical study on the axisymmetric contact and adhesive behaviors of a transversely isotropic piezoelectric half-space under a rigid punch, with an emphasis on Hertzian contact and JKR-type adhesion solutions for the conducting punch of power-law profile. The Hertzian piezoelectric contact model and JKR-type adhesion model are established by cumulative superposition and equivalent energy release rate approaches, respectively. Closed-form expressions are derived for the applied load, indentation depth, distributions of contact traction and surface displacement, which are able to link existing solutions for non-adhesive and adhesive contact problems for transversely isotropic and isotropic elastic materials, and to include the corresponding Hertz-n and JKR-n solutions as special cases. Similar mathematical forms are found between the elastic solids and the piezoelectric materials under a conducting grounded punch except for different material moduli. These results can serve as benchmarks for checking the validity of numerical methods.