### Abstract

We consider a specific class of nonlinear homogenization problems. The microstructure is a sort of checkerboard polycrystal, and the energy of the basic crystal is degenerate in one direction. We give matching upper and lower bounds for the homogenized energy. The motivation for this problem lies in the recent work of Bhattacharya & Kohn on shape-memory polycrystals. Our results show that a bound proved therein is nearly sharp.

Original language | English (US) |
---|---|

Pages (from-to) | 567-583 |

Number of pages | 17 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 455 |

Issue number | 1982 |

State | Published - 1999 |

### Fingerprint

### Keywords

- checkerboard microstructure
- homogenization
- optimal bounds
- shape-memory polycrystals

### ASJC Scopus subject areas

- General

### Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*455*(1982), 567-583.

**Some examples of nonlinear homogenization involving nearly degenerate energies.** / Bhattacharya, K.; Kohn, Robert; Kozlov, S.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 455, no. 1982, pp. 567-583.

}

TY - JOUR

T1 - Some examples of nonlinear homogenization involving nearly degenerate energies

AU - Bhattacharya, K.

AU - Kohn, Robert

AU - Kozlov, S.

PY - 1999

Y1 - 1999

N2 - We consider a specific class of nonlinear homogenization problems. The microstructure is a sort of checkerboard polycrystal, and the energy of the basic crystal is degenerate in one direction. We give matching upper and lower bounds for the homogenized energy. The motivation for this problem lies in the recent work of Bhattacharya & Kohn on shape-memory polycrystals. Our results show that a bound proved therein is nearly sharp.

AB - We consider a specific class of nonlinear homogenization problems. The microstructure is a sort of checkerboard polycrystal, and the energy of the basic crystal is degenerate in one direction. We give matching upper and lower bounds for the homogenized energy. The motivation for this problem lies in the recent work of Bhattacharya & Kohn on shape-memory polycrystals. Our results show that a bound proved therein is nearly sharp.

KW - checkerboard microstructure

KW - homogenization

KW - optimal bounds

KW - shape-memory polycrystals

UR - http://www.scopus.com/inward/record.url?scp=33645474376&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645474376&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33645474376

VL - 455

SP - 567

EP - 583

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

IS - 1982

ER -