Extended Model of Surface-Related Effects in Second-Gradient Elasticity. Surface Waves Related to the Nature of Adhesion

Abstract

It is considered a continuum theory of the adhesion properties of the surface of elastic bodies, which can be considered as theory of surface elasticity. We consider the surface of the body as the set of all the boundary points of the elastic body and believe that upon deformation, this surface is endowed with its own density of surface energy in the case of an adhesion-active surface. The definition of the “ideal” and gradient theory of elasticity of surface interactions is given, and it is shown that the ideal adhesion theory constructed by Gurtin and Murdoch, taking into account the properties of symmetry and material indifference, is far from complete. The work gives a fairly broad generalization of the surface-related theory of elastic bodies. The statements of the problems of propagation of surface waves on the adhesion-active surface of the classical elastic half-space are considered. We considered five types of surface waves that are attractive from the point of view of experimental determination of the characteristics of adhesive interactions and found that these types of surface waves could not be existed for the classical theory of elasticity with adhesion-passive surfaces, where moduli of the adhesion interactions are equal zero. The first three of these types of waves are associated separately with each of the three components of the surface displacement vector. The fourth and fifth types of surface waves are associated, respectively, with the field of local changes in the surface area and with the field of its local rotations with a vector that coincides with the normal to the surface.