Investigation of frictional sliding contact problems of triangular and cylindrical punches on monoclinic piezoelectric materials

• A frictional sliding contact model for monoclinic piezoelectric materials is established.
• Fundamental solutions that can lead to real values of physical quantities are given.
• The exact solution of the reduced singular integral equation is presented.
• Closed-form expressions of various surface stresses and electric displacement are given.
• Surface damage mechanism of monoclinic piezoelectric materials is revealed.

A theoretical model of a frictional sliding contact problem for monoclinic piezoelectric materials under triangular and cylindrical punches is established. The characteristic equation related to the governing equations of monoclinic piezoelectric materials is of eight-order, which generates real and/or complex eigenvalues. Fundamental solutions that can lead to real values of physical quantities are given for both real and complex eigenvalues. By applying Fourier transform, the mixed boundary value problem is reduced to a singular integral equation of the second kind of Cauchy type. Based on exact solutions of the reduced singular integral equation, closed-form expressions of various surface stresses and electric displacement are obtained. Moreover, relations between the applied load and the contact region are obtained. Numerical results are given to show the influences of the friction coefficient on various surface stresses, electric displacement and even the width of the contact region. The underlying physics/mechanics accounting for the observations are presented.