Implementation of surface effects in three kinds of finite bending

This paper demonstrates the methodology for implementing surface elasticity and surface tension in pure bending representatives of the well-known large deformation families: bending of a rectangular block, bending of one cylindrical sector into another sector of a different curvature and straightening of a cylindrical sector. Constitutive equations based on the surface energy decoupling are proposed to model the surface behavior. Changes in mechanical response of hyperelastic bodies at smaller scales, particularly surface effects on the resultant force, resultant moment and bending stiffness are analyzed for the special case of a neo-Hookean solid and found to be consistent in all three pure bending problems.