### Abstract

Dislocation density based modeling of crystal plasticity remains one of the central challenges in multi scale materials modeling. A dislocation based theory requires sufficiently rich dislocation density measures which are capable of predicting their own evolution. Continuum dislocation dynamics is based on a higher dimensional dislocation density tensor comprised of two distribution functions on the space of local orientations, which are the density of dislocations per orientation and the density of dislocation curvature per orientation. We propose to expand these functions into series of symmetric tensors (alignment tensors), to be used in dislocation based theories without extra dimensions. The first two terms in the expansion of the density define the total dislocation density and the Kröner-Nye tensor. The first term in the expansion of the curvature density, the scalar total curvature density, turns out to be a conserved quantity; the integral of which corresponds to the total number of dislocations. The content of the next higher order tensors is discussed.

Original language | English |
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Title of host publication | Proceedings of the Multiscale Materials Modeling 2012 Conference |

Publisher | Materials Research Society |

Pages | 1-7 |

Number of pages | 7 |

Volume | 1535 |

ISBN (Print) | 9781632661258 |

DOIs | |

Publication status | Published - 2013 |

Event | 21st International Materials Research Congress, IMRC 2012 - Cancun, Mexico Duration: 12 Aug 2012 → 17 Aug 2012 |

### Conference

Conference | 21st International Materials Research Congress, IMRC 2012 |
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Abbreviated title | IMRC 2012 |

Country | Mexico |

City | Cancun |

Period | 12/08/12 → 17/08/12 |

### Fingerprint

### ASJC Scopus subject areas

- Materials Science(all)
- Condensed Matter Physics
- Mechanical Engineering
- Mechanics of Materials

### Cite this

*Proceedings of the Multiscale Materials Modeling 2012 Conference*(Vol. 1535, pp. 1-7). Materials Research Society. https://doi.org/10.1557/opl.2013.451

**Higher order alignment tensors for continuum dislocation dynamics.** / Hochrainer, Thomas.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

*Proceedings of the Multiscale Materials Modeling 2012 Conference.*vol. 1535, Materials Research Society, pp. 1-7, 21st International Materials Research Congress, IMRC 2012, Cancun, Mexico, 12/08/12. https://doi.org/10.1557/opl.2013.451

}

TY - GEN

T1 - Higher order alignment tensors for continuum dislocation dynamics

AU - Hochrainer, Thomas

PY - 2013

Y1 - 2013

N2 - Dislocation density based modeling of crystal plasticity remains one of the central challenges in multi scale materials modeling. A dislocation based theory requires sufficiently rich dislocation density measures which are capable of predicting their own evolution. Continuum dislocation dynamics is based on a higher dimensional dislocation density tensor comprised of two distribution functions on the space of local orientations, which are the density of dislocations per orientation and the density of dislocation curvature per orientation. We propose to expand these functions into series of symmetric tensors (alignment tensors), to be used in dislocation based theories without extra dimensions. The first two terms in the expansion of the density define the total dislocation density and the Kröner-Nye tensor. The first term in the expansion of the curvature density, the scalar total curvature density, turns out to be a conserved quantity; the integral of which corresponds to the total number of dislocations. The content of the next higher order tensors is discussed.

AB - Dislocation density based modeling of crystal plasticity remains one of the central challenges in multi scale materials modeling. A dislocation based theory requires sufficiently rich dislocation density measures which are capable of predicting their own evolution. Continuum dislocation dynamics is based on a higher dimensional dislocation density tensor comprised of two distribution functions on the space of local orientations, which are the density of dislocations per orientation and the density of dislocation curvature per orientation. We propose to expand these functions into series of symmetric tensors (alignment tensors), to be used in dislocation based theories without extra dimensions. The first two terms in the expansion of the density define the total dislocation density and the Kröner-Nye tensor. The first term in the expansion of the curvature density, the scalar total curvature density, turns out to be a conserved quantity; the integral of which corresponds to the total number of dislocations. The content of the next higher order tensors is discussed.

UR - http://www.scopus.com/inward/record.url?scp=84900312977&partnerID=8YFLogxK

U2 - 10.1557/opl.2013.451

DO - 10.1557/opl.2013.451

M3 - Conference contribution

SN - 9781632661258

VL - 1535

SP - 1

EP - 7

BT - Proceedings of the Multiscale Materials Modeling 2012 Conference

PB - Materials Research Society

ER -