Surface Green function for a soft elastic half-space: Influence of surface stress

Surface Green function for incompressible, elastically isotropic half-space coupled with surface stress is derived by using double Fourier transform technique. The result indicates that the surface displacement induced by a force tangential to the surface is the same as the usual solution for elastic half-spaces where the effect of surface stress is ignored. However, the displacement caused by a force normal to the surface involves an additional parameter, i.e. the ratio of specific surface stress to shear modulus. The parameter has the dimension of length, and may provide a means to introduce an intrinsic length scale for some related problems regarding the surface of an elastic half-space. This is extremely true for soft elastic media with very low shear modulus, because in that situation the magnitude of the parameter is relatively large. As an illustrative example, the proposed Green function is adopted to analyze the interaction between two molecules with circular section adsorbed on the surface of a soft elastic half-space. It is shown that surface stress remarkably affects the pair interaction potential when the distance between the molecules is not larger than several times of the intrinsic length scale.