Elastic interaction between force dipoles on a stretchable substrate

The objective of this paper is to study elastic interaction between force dipoles on the surface of a semi-infinite stretchable substrate. The substrate undergoes a uniform, finite pre-stretch, while the additional deformation induced by a force dipole is assumed infinitesimal. By adopting a neo-Hookean constitutive law, the surface Green function for the pre-stretched substrate is obtained. The result is then used to derive the energy of dipolar interaction on the surface. As an application, mutual interaction between two physisorbed molecules is discussed in detail. The dipole moment of a molecule is found from the elementary intermolecular potential, and its dependence on the pre-stretch is established explicitly. Numerical results indicate that pre-stretches can substantially alter the interaction, and thus provide a controllable way to guide the self-assembly of adsorbed molecules on the substrate surface.