Elastic solution of surface loaded layer with couple and surface stress effects

Area of Science:

• Solid Mechanics
• Materials Science
• Nanotechnology

Background:

• Traditional elastic solutions often neglect surface stress and microstructural effects.
• These effects become significant at the micro/nano scale, influencing material behavior.
• Contact mechanics at small scales requires advanced theoretical frameworks.

Purpose of the Study:

• To establish an elastic solution for axisymmetrically surface-loaded thin layers on a rigid substrate.
• To incorporate surface stress and material microstructural effects into the elastic solution.
• To investigate the size effects on mechanical response and provide fundamental solutions for micro/nano-scale contact problems.

Main Methods:

• Adoption of couple stress theory for the bulk layer and surface elasticity theory for the surface material.
• Utilizing the Hankel transform method to derive the general solution of the elastic field within the bulk layer.
• Integration of surface equations and boundary conditions to determine unknown constants.

Main Results:

• An elastic solution accounting for surface and couple stresses was successfully established.
• The derived solutions enable the investigation of size effects on mechanical responses.
• The study provides fundamental solutions applicable to micro/nano-scale contact mechanics.

Conclusions:

• Surface stress and couple stress significantly influence the load transfer mechanism to the substrate.
• The mechanical response exhibits size-dependent characteristics across various external and internal length scales.
• The developed solutions are essential for accurate modeling of micro/nano-scale contact phenomena.