A note on the optimal state of a binary solid mixture in a stressed elastic bar

Roger Fosdick, Gianni F. Royer-Carfagni, Hans F Weinberger

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We consider the potential energy of the equlibrium configuration under gravity and prescribed vertical forces or displacement of a vertical bar which is composed of a mixture of two elastic materials. It is supposed that in each horizontal cross section the mixture has an effective Young's modulus which depends only on the ratio of the two materials in that cross section, and that the dependence satisfies the bound of Paul [2]. It is shown that among all arrangements of the constituents with a given volume fraction, the smallest potential energy is attained when one of the materials is segregated in a single horizontal layer. This result suggests that when a composite cylinder is kept in such a state of strain, its constituent material will eventually diffuse into this segregated state.

Original languageEnglish (US)
Pages (from-to)519-525
Number of pages7
JournalMeccanica
Volume31
Issue number5
DOIs
StatePublished - Jan 1 1996

Keywords

  • Bar
  • Elasticity
  • Phase equilibrium
  • Thermomechanics of continua

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