On the Stability of a Mixture of Two Elastic Solids

Abstract

We consider the stability of a mixture of two anisotropic linear elastic solids, which possesses internal friction due to the mechanical interaction between the solids. The interest in such a mixture lies in its possible application to binary alloys and to some composite materials. Further, since a pure metallic specimen is often difficult to obtain, many metals may actually consist of two or more metallic solids. It is shown that in general such a mixture will be asymptotically stable under mixed boundary conditions when certain definiteness conditions are imposed on the coefficients, even when the temperature remains constant. Instability of the mixture is also discussed and we then show that by imposing a boundedness condition on the solution stability can be recovered under very much less restrictive conditions on the coefficients.