Alloy separation of a binary mixture in a stressed elastic sphere
An isotropic binary linear-elastic spherical solid mixture subject to a given constant radial displacement along its boundary is analyzed. The two material parameters are assumed to depend on the volumetric concentration \(c\) of the mixture. The spherical symmetric spatial distribution of \(c\) is sought under the condition of minimizing the total potential energy \(E\) with respect to \(c\) and the radial displacement. As \(E\) turns out to be neither lower semicontinuous nor coercive, a related auxiliary minimization problem for a hollow sphere (a small ball being deleted from the original sphere) is considered which enjoys these properties. Thus a minimizing displacement and concentration field exists which is shown to minimize also the original \(E\) and to yield a unique solution. It is found that in the optimal state the two component materials are separated into two parts: the central core containing the ``hard material'', and the remaining layer containing the ``soft material''.
scientific article; zbMATH DE number 911939