An approximate analytical solution for shear traction in partial reverse slip contacts

Singular integral equations solved to obtain a closed-form shear distribution under partial reverse slip conditions involve the integration of contact pressure over a sub-domain of the contact region. Pressure distribution for a nominal flat contact contains logarithmic terms, which pose difficulty in solving these integral equations. This paper provides a simpler approximation to the pressure distribution for a symmetrical nominally flat punch in contact with an elastic half-space to overcome this difficulty. Taylor series approximation has been used in the central flat and curved regions to approximate the nominally flat contact pressure distribution to a square flat (with sharp corners) and Hertzian pressure forms, respectively. The approximation is valid over the entire domain and for any ratio of contact length to flat length. The approximated pressure is used to evaluate the necessary singular integrals for the analytical solution for shear traction under partial reverse slip conditions while being subjected to bulk stress.