Response of bimaterials with interfacial tension subjected to axisymmetric body force

Abstract

This paper presents an analytical treatment of the boundary value problem of an isotropic elastic bimaterial full space with interfacial tension subjected to an axisymmetric body force. The interfacial tension is modeled as the residual stress in the pre-tensed interfacial atom membrane on the basis of Gurtin and Murdoch's surface theory. The generality of the present model is justified with several degenerated cases (e.g. classical bimaterials with bonded and unsinkable interface, homogeneous full space with interfacial tension, and half space with surface tension). By virtue of classical Hankel or Fourier transforms, the unconventional boundary value problems are addressed in a concise and systematic manner. The final solutions are all given in the form of a semi-infinite line integral. Particularly, the solutions for the interfacial response induced by interfacial point load can be obtained in exact closed form in terms of Struve and Bessel functions. Numerical results are presented to show the influence of interfacial tension on the induced responses. It is shown that the existence of interfacial tension can significantly influence the induced elastic fields and reduce the point load singularity. The results presented in this paper are useful and meaningful to the studies of nanocomposites, soft solids, and biological tissue, where the effects of surface/interface tension could be dominant.