EXISTENCE THEOREMS IN THE THEORY OF MIXTURES

This paper is concerned with boundary-value problems of the linear the ory for binary mixtures of elastic bodies. First, a counterpart of the Boussinesq-Somigliana-Galerkin solution in classical elastostatics is established and the fundamental solutions in the equilibrium theory o f homogeneous and isotropic mixtures are derived. Then, representation s of Somigliana type for the displacement fields are presented. The po tentials of single layer and double layer are used to reduce the bound ary-value problems to singular integral equations. Existence and uniqu eness results are established.