Surface viscoelasticity and effective properties of thin-walled structures at the nanoscale

We discuss the influence of surface viscoelasticity effects on the effective properties of materials such as effective bending stiffness of plates or shells. Viscoelastic properties in the vicinity of the surface can differ from the properties of the bulk material. This difference influences the behavior of nanostructural elements. In particular, the surface viscoelastic stresses are responsible for the size-depended dissipation of nanosized structures. Using the extension of the Gurtin–Murdoch model and the correspondence principle of linear viscoelasticity we derive the expressions of the stress and couple stress resultant tensors for shear deformable plates and shells.