# Frictional half-plane contact problems subject to alternating normal and shear loads and tension in the steady state

## TL;DR

This paper analyzes steady-state frictional contact problems between elastic bodies under combined constant and oscillatory normal, shear, and tension loads, explicitly determining the stick and slip zones.

## Contribution

It provides explicit formulas and methods for identifying the maximum slip zones in symmetric half-plane contact problems with friction under complex loading.

## Key findings

- Explicit stick zone boundaries are derived.
- Approximate solutions are developed for practical application.
- The analysis covers combined normal, shear, and tension loads in steady state.

## Abstract

The problem of a general, symmetric contact, between elastically similar bodies, and capable of idealisation using half-plane theory, is studied in the presence of interfacial friction. It is subject to a constant set of loads - normal force, shear force and bulk tension parallel with the interface - together with an oscillatory set of the same quantities, and is in the steady state. Partial slip conditions are expected to ensue for a range of these quantities, and the permanent stick zone is explicitly established, thereby effectively specifying the maximum extent of the slip zones. Exact and approximate, easy to apply recipes are obtained.