Papkovich–Neuber solution for a mixture of two elastic solids and Kelvin problem

Abstract

First, the equations of equilibrium are transformed into a more generalized form of Navier’s equations using the linearized constitutive equations for a mixture of two elastic solids which are given by Green and Steel. Second, these new Navier’s equations are solved by the Papkovich–Neuber method. Finally, the Kelvin’s problem of an infinite mixture of two elastic solids, under a single force acting in the interior of the mixture, is solved.