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

Robert Kohn, Barbara Niethammer

Research output: Contribution to journalArticle

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
StatePublished - Mar 2000

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Polycrystal
Shape Memory
Polycrystals
Shape memory effect
Crystal symmetry
Sufficient
Symmetry
Linear Elasticity
Elastic Material
Percent
Elasticity
Predict

Keywords

  • Nonlinear homogsnization
  • Recoverable strain
  • Shape memory polycrystals

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Applied Mathematics
  • Modeling and Simulation

Cite this

Geometrically nonlinear shape-memory polycrystals made from a two-variant material. / Kohn, Robert; Niethammer, Barbara.

In: Mathematical Modelling and Numerical Analysis, Vol. 34, No. 2, 03.2000, p. 377-398.

Research output: Contribution to journalArticle

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