Geometrically nonlinear shape-memory polycrystals made from a two-variant material

Robert V. Kohn, Barbara Niethammer

Research output: Contribution to journalArticlepeer-review

Abstract

Bhattacharya and Kohn have used small-strain (geometrically linear) elasticity to analyze the recoverable strains of shape-memory polycrystals. The adequacy of small-strain theory is open to question, however, since some shape-memory materials recover as much as 10 percent strain. This paper provides the first progress toward an analogous geometrically nonlinear theory. We consider a model problem, involving polycrystals made from a two-variant elastic material in two space dimensions. The linear theory predicts that a polycrystal with sufficient symmetry can have no recoverable strain. The nonlinear theory corrects this to the statement that a polycrystal with sufficient symmetry can have recoverable strain no larger than the 3/2 power of the transformation strain This result is in a certain sense optimal. Our analysis makes use of Fritz John's theory of deformations with uniformly small strain.

Original languageEnglish (US)
Pages (from-to)377-398
Number of pages22
JournalMathematical Modelling and Numerical Analysis
Volume34
Issue number2
DOIs
StatePublished - 2000

Keywords

  • Nonlinear homogsnization
  • Recoverable strain
  • Shape memory polycrystals

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modeling and Simulation
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Geometrically nonlinear shape-memory polycrystals made from a two-variant material'. Together they form a unique fingerprint.

Cite this