Static fundamental solutions for a bi-material full-space

In this paper, the complete static response of two joined dissimilar half-spaces due to an arbitrary interior point load is derived. By means of a method of displacement potentials and integral transforms, a dual format of the solution in the form of a Hankel integral representation and algebraic closed-form expressions is presented. As illustrations, its analytical degeneration to benchmark solutions for a homogeneous medium as well as its variation under general geometric and material conditions are shown. The importance of the dual format of the bi-material solution in connection with the method of asymptotic decomposition to the development of a rigorous treatment of its dynamic counterpart is also demonstrated.