# Shear-induced contact area anisotropy explained by a fracture mechanics model

## TL;DR

This paper develops a fracture mechanics model to explain shear-induced anisotropy in adhesive contact areas, validated against experimental data, and predicts the influence of punch geometry on contact behavior.

## Contribution

It introduces a novel fracture mechanics model with mode-mixity functions to describe anisotropic contact behavior under shear, extending previous adhesion models to elliptical contacts.

## Key findings

- Model accurately predicts experimental observations.
- Punch geometry influences contact area shape and decay.
- Mode-mixity functions effectively describe mode coupling.

## Abstract

This paper gives a theoretical analysis for the fundamental problem of anisotropy induced by shear forces onan adhesive contact, discussing the experimental data of the companion Letter. We present a fracture mechanicsmodel where two phenomenological mode-mixity functions are introduced to describe the weak couplingbetween modes I and II or I and III, which changes the effective toughness of the interface. The mode-mixityfunctions have been interpolated using the data of a single experiment and then used to predict the behavior of thewhole set of experimental observations. The model extends an idea by Johnson and Greenwood, to solve purelymode I problems of adhesion in the presence of a nonaxisymmetric Hertzian geometry, to the case of ellipticalcontacts sheared along their major or minor axis. Equality between the stress intensity factors and their criticalvalues is imposed solely at the major and minor axes. We successfully validate our model against experimentaldata. The model predicts that the punch geometry will affect both the shape and the overall decay of the shearedcontact area.