Coupling of surface effect and hyperelasticity in combined tension and torsion deformations of a circular cylinder

During the past decade there has been increasing research into the role of surface mechanics which can be relevant for many of today's elastomeric applications. This paper incorporates surface effects into large deformation elasticity for a well-known continuum model of a circular cylinder under combined torsion and tension loadings and thus, generalizes it for application at smaller scales, such as nano- and micro-scales. At these scales, the effect of the surface and residual surface stresses on the overall deformation of the bulk material is of critical importance. The proposed model employs the Gurtin-Murdoch theory to represent the surface effect as a residually prestressed thin hyperelastic film of separate elasticity, perfectly bonded to the bulk. Using a constitutive model for which analytical solution can be derived, we demonstrate the pronounced effect of the surface and residual surface stresses not only on the values of resultant axial force and twisting moment, but also on the axial stiffness, the torsional rigidity and the Poynting effect.