Influence of boundary elasticity on a couple stress elastic solid with a mode-III crack

Abstract

In this article, we develop a linear theory of elastic boundary reinforcement of a couple stress elastic solid subjected to anti-plane deformations. The reinforcement is represented by a thin couple stress elastic coating perfectly bonded to the boundary of the solid. The elastic properties of the coating are taken to be separate from those of the surrounding bulk material. In this context, the model developed here can also be viewed as a more comprehensive representation of the deformation of a couple stress material in which the separate role of surface mechanics is incorporated into the model of deformation. As an example of our theory, we consider the classical problem of a semi-infinite crack in a couple stress material and examine the contribution of the reinforcement to the stress distributions in the vicinity of the crack tip. Our results indicate that the presence of the reinforcing layer on the crack faces eliminates the well-known stress singularity at the crack tip demonstrating the influence of surface and couple stress effects in the model of deformation.