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AbstractÐA general theory is presented for the axisymmetric indentation of piezoelectric solids within the context of fully coupled, transversely isotropic elasticity models. Explicit expressions for P±h curves are derived for spherical, conical as well as cylindrical punch indenter geometries in a manner that can be directly related to the experimental measurements. In addition, results for dierent electrical boundary conditions that employ conducting or insulating indenters are also presented. The theory reveals that the indentation load vs penetration depth, and the contact area vs penetration depth relations have the same mathematical structure as the classical elastic indentation problem. It is, however, demonstrated that the electric ®eld induced during indentation as a result of the electrical±mechanical coupling can resist or aid in the penetration of the indenter into the piezoelectric material depending on the electrical conductivity of the indenter and the surface boundary conditions of the indented substrate. It is also shown that the piezoelectric material exhibits pile-up or sink-in of material around the indenter as a consequence of electromechanical coupling, despite the absence of any inelastic deformation processes or strain hardening. The theoretical predictions are corroborated with detailed ®nite-element simulations for dierent indenter geometries. The theoretical results facilitate the prediction of some transient electrical eects which can be used in conjunction with experiments for the estimation of some of the elastic, dielectric and piezolectric constants during instrumented indentation. Speci®c examples and details of such applications are addressed in separate papers. #

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