title: A closed form large deformation solution of plate bending with surface effects.
abstract: We study the effect of surface stress on the pure bending of a finite thickness plate under large deformation. The surface is assumed to be isotropic and its stress consists of a part that can be interpreted as a residual stress and a part that stiffens as the surface increases its area. Our results show that residual surface stress and surface stiffness can both increase the overall bending stiffness but through different mechanisms. For sufficiently large residual surface tension, we discover a new type of instability - the bending moment reaches a maximum at a critical curvature. Effects of surface stress on different stress components in the bulk of the plate are discussed and the possibility of self-bending due to asymmetry of the surface properties is also explored. The results of our calculations provide insights into surface stress effects in the large deformation regime and can be used as a test for implementation of finite element methods for surface elasticity.
authors.affiliation: Field of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14850, USA. ch45@cornell.edu.
authors.forename: Tianshu
authors.initials: T
authors.lastname: Liu
authors.affiliation: Department of Chemical and Biomolecular Engineering and Bioengineering Program, Lehigh University, Bethlehem, PA 18015, USA.
authors.forename: Anand
authors.initials: A
authors.lastname: Jagota
authors.affiliation: Field of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14850, USA. ch45@cornell.edu.
authors.forename: Chung-Yuen
authors.initials: CY
authors.lastname: Hui