Higher order alignment tensors for continuum dislocation dynamics

Thomas Hochrainer*

*Korrespondierende/r Autor/in für diese Arbeit

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem Konferenzband


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.

TitelProceedings of the Multiscale Materials Modeling 2012 Conference
Herausgeber (Verlag)Materials Research Society
ISBN (Print)9781632661258
PublikationsstatusVeröffentlicht - 2013
Veranstaltung21st International Materials Research Congress - Cancun, Mexico
Dauer: 12 Aug 201217 Aug 2012


Konferenz21st International Materials Research Congress
KurztitelIMRC 2012

ASJC Scopus subject areas

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

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  • Dieses zitieren

    Hochrainer, T. (2013). Higher order alignment tensors for continuum dislocation dynamics. in Proceedings of the Multiscale Materials Modeling 2012 Conference (Band 1535, S. 1-7). Materials Research Society. https://doi.org/10.1557/opl.2013.451