Fundamental solutions for bimaterials with inextensible interface

Abstract

Fundamental solutions are obtained in exact closed forms for elastic fields in bimaterial elastic solids with a horizontally inextensible interface and differing transversely isotropic properties induced by concentrated points and ring-force vectors. For the concentrated point-force vector, the fundamental solution is expressed in terms of elementary harmonic functions. For the concentrated ring-force vector, the fundamental solution is expressed in terms of the complete elliptic integral of the first, second, and third kinds. Numerical results are presented to illustrate the effect of anisotropic bimaterial properties on the transmission of normal contact stress and the discontinuity of shear contact stress at the horizontally inextensible interface. The closed-form solutions are systematically presented in matrix forms that can be easily implemented in numerical schemes, such as boundary-element methods to solve elastic problems in engineering mechanics.