Action of a smooth flat charged punch on the piezoelectric half-space possessing symmetry of class 6

The paper focuses on the problem of indentation of a piezoelectric half-space of symmetry of class 6 by a flat charged indenter of arbitrary shape accompanied by frictionless sliding. The research is motivated by needs in scanning probe microscopy for bone tissue and its components. The problem is solved using method of potential functions. First we solve the auxiliary problem about action of point forces normal and tangential to the boundary of the half-space and point electric charge. Solution is compared with the known one for symmetry class 6 mm. Then this result is used to construct explicit solution for a flat charged punch of arbitrary shape. To the best of our knowledge, analytical solution of this kind has never been constructed for piezoelectric materials of the symmetry class 6—only for the particular case of symmetry 6 mm.