The Effect of Small Viscous Inclusions on the Mechanical Properties of an Elastic Solid

As a guide to the interpretation of observed viscoelastic effects in solids that are almost ideally elastic, it is of interest to calculate what the effect would be, on mechanical properties, of local imperfections of different kinds distributed throughout an otherwise elastic solid. The presence of any flaws where work is done against internal friction when the material as a whole is deformed will give rise to delayed elastic response, and to energy losses when the material is subjected to varying deformations, for example during vibrations. To make the theoretical problem tractable, so that a quantitative answer can be obtained, it is necessary to consider a somewhat over-simplified picture of the type of imperfection which might arise in practice. In the present paper, what appears to be the simplest possible model of a visco-elastic solid is discussed.