Surface finite viscoelasticity and surface anti-plane waves

We introduce the surface viscoelasticity under finite deformations. The theory is straightforward generalization of the Gurtin–Murdoch model to materials with fading memory. Surface viscoelasticity may reflect some surface related creep/stress relaxation phenomena observed at small scales. Discussed model could also describe thin inelastic coatings or thin interfacial layers. The constitutive equations for surface stresses are proposed. As an example we discuss propagation shear (anti-plane) waves in media with surface stresses taking into account viscoelastic effects. Here we analysed surface waves in an elastic half-space with viscoelastic coatings. Dispersion relations were derived.