Derivation of Full Elastic Fields for Force Doublets Near an Interface Between Two Materials

Plane elasticity solutions for concentrated forces near a welded interface between two materials can be used for a variety of purposes, among them, the derivation of elastic fields for force doublets (dipoles) or nuclei of strain. The objective of this work is to derive and record the full elastic fields for the force doublets near an interface between two materials. The solutions are exact within the classical theory of elasticity, and are in closed form in terms of elementary functions. Explicit formulae are given for the Airy stress functions, the components of stress and displacement, and the tractions on the interface (in Cartesian co-ordinates).