Johnson-Kendall-Roberts adhesive contact for a toroidal indenter

Area of Science:

• Solid Mechanics
• Materials Science
• Adhesion Science

Background:

• Adhesive contact mechanics is crucial for understanding material interactions.
• The Johnson-Kendall-Roberts (JKR) theory provides a framework for analyzing adhesive contact.
• Toroidal indenters present unique geometric challenges in contact analysis.

Purpose of the Study:

• To investigate the unilateral axisymmetric frictionless adhesive contact problem for a toroidal indenter on an elastic half-space.
• To derive asymptotic solutions for different contact area configurations.
• To analyze the influence of elastic properties on pull-off force.

Main Methods:

• Application of the Johnson-Kendall-Roberts (JKR) theory.
• Derivation of asymptotic solutions for semi-fixed and variable annular contact areas.
• Detailed analysis of Barber's concave indenter and v-shaped generalized toroidal indenters.

Main Results:

• An asymptotic solution was obtained for a semi-fixed annular contact area, building upon non-adhesive contact solutions.
• A leading-order asymptotic solution was constructed for a narrow annular contact area with variable radii.
• The pull-off force for a v-shaped generalized toroidal indenter was found to be independent of the elastic properties of the indented solid.

Conclusions:

• Asymptotic solutions can be effectively derived for adhesive contact problems involving toroidal indenters.
• The independence of pull-off force from elastic properties for specific toroidal indenters offers valuable insights for material design and application.
• This research contributes to a deeper understanding of adhesive contact phenomena in complex geometries.