Alloy separation of a binary mixture in a stressed elastic sphere
type: Item
instance of: scholarly article
title: Alloy separation of a binary mixture in a stressed elastic sphere
zbMATH Open document ID: 0864.73016
DOI: 10.1007/BF00041223
author: Gianni Royer-Carfagni
author: Roger Fosdick
published in: Journal of Elasticity
publication date: 1996-07-31T00:00:00Z
review text: 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''.
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
zbMATH DE Number: 911939
zbMATH Keywords: hard material
zbMATH Keywords: soft material
zbMATH Keywords: radial displacement
zbMATH Keywords: volumetric concentration
zbMATH Keywords: total potential energy
zbMATH Keywords: minimization problem
zbMATH Keywords: hollow sphere
zbMATH Keywords: unique solution
reviewed by: Hans Bufler
MaRDI profile type: Publication
cites work: The static state of a two-phase solid mixture in a stressed elastic bar
cites work: A note on the optimal state of a binary solid mixture in a stressed elastic bar
cites work: On Lower Semicontinuity of Integral Functionals. II
description: scientific article; zbMATH DE number 911939