General interface conditions in surface elasticity of nanoscaled solids in general curvilinear coordinates

We consider an arbitrarily curved three-dimensional thin interphase with surface stresses between two anisotropic solids. Letting the interphase be infinitely thin and assuming that the kinematic constraints between the two anisotropic solids remain intact during the deformation, we derive the interface jump conditions along the interface. These conditions are derived analytically in general non-orthogonal curvilinear coordinates in the setting of linear elasticity and steady state conduction. The proof is made directly from a force balance consideration of a small element of the curved interface. Simplified results are also deduced for oblique coordinate systems in which the coordinate axes are straight lines that are not perpendicular to each other. When the axes are orthonormal, we prove that our results agree with the previous known Young-Laplace conditions in solids.