A closed form large deformation solution of plate bending with surface effects

Area of Science:

• Solid Mechanics
• Materials Science
• Surface Physics

Background:

• Surface stress significantly influences the mechanical behavior of thin films and small structures.
• Understanding large deformation effects is crucial for micro/nanoscale device applications.
• Existing models often neglect the coupled effects of residual stress and surface area stiffening.

Purpose of the Study:

• To investigate the impact of surface stress on the pure bending of finite thickness plates under large deformation.
• To differentiate the contributions of residual surface stress and surface area stiffening to bending stiffness.
• To identify novel phenomena, such as instabilities, arising from surface stress effects.

Main Methods:

• Development of a theoretical model incorporating isotropic surface stress with residual and area-dependent components.
• Analysis of pure bending under large deformation conditions.
• Numerical calculations to explore stress distributions and stability criteria.

Main Results:

• Both residual surface stress and surface area stiffening increase the overall bending stiffness.
• A new instability is identified: the bending moment reaches a maximum at a critical curvature for large residual surface tension.
• Surface stress asymmetry can lead to self-bending effects.

Conclusions:

• Surface stress plays a critical role in the large deformation bending of plates.
• The study reveals distinct mechanisms by which residual stress and surface stiffening affect bending stiffness.
• The findings offer insights for advanced material design and validation of computational methods in surface elasticity.