Finite element simulation of the effect of electric boundary conditions on the spherical indentation of transversely isotropic piezoelectric films

Finite element simulation was used to analyze the effect of electric boundary conditions on the indentation deformation of a transversely isotropic piezoelectric film with the contact radius much larger than the film thickness. Six different combinations of electric boundary conditions were used. The simulation results showed that the indentation load is proportional to the square of the indentation depth and the indentation-induced electric potential at the contact center is a linear function of the ratio of the indentation depth to the film thickness for all six cases. The contact stiffness is proportional to the contact area and inversely proportional to the film thickness. The nominal piezoelectric charge coefficient d ₃₃ is inversely proportional to the derivative of the electric potential with respect to the indentation depth for the indentation of a piezoelectric film by a conducting indenter with a grounded, rigid substrate.