## 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 language | English (US) |
---|---|

Pages (from-to) | 377-398 |

Number of pages | 22 |

Journal | Mathematical Modelling and Numerical Analysis |

Volume | 34 |

Issue number | 2 |

DOIs | |

State | Published - 2000 |

## Keywords

- Nonlinear homogsnization
- Recoverable strain
- Shape memory polycrystals

## ASJC Scopus subject areas

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