Piezoelectric indentation of a flat circular punch accompanied by frictional sliding and applications to scanning probe microscopy

Indentation of a piezoelectric half-space by a flat circular indenter accompanied by frictional sliding is considered. Full-field electroelastic solutions in elementary functions are obtained. The solution is based on the correspondence principle between elastic and piezoelectric problems. Stiffness relations between applied load and resulting displacement are given in elementary functions. In conjunction with the conical and spherical solutions, given previously by Makagon et al. [A. Makagon, M. Kachanov, S.V. Kalinin, E. Karapetian, Indentation and frictional sliding of spherical and conical punches into piezoelectric half-space, Physical Review B 76 (2007) 064115 (14)], this work completes the set of limiting cases of tip geometries utilized in lateral force microscopy (LFM) technology. Implications for quantitative interpretation of scanning probe microscopy (SPM) data and tribological data are analyzed.