Moving dislocations in finite plasticity: a topological approach

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

Abstract

Plastic deformation of crystals is mostly mediated by the motion of dislocations. During the last two decades a lot of effort was directed towards including more knowledge about dislocations in continuum descriptions of plasticity. Promising approaches towards building continuum plasticity theories on averages of the behavior of many single dislocations have been formulated under the assumption of small deformations. In the current paper we derive the kinematics of single dislocations moving inside a dislocated crystal simultaneously deforming by the motion of other dislocations in the language of large deformation plasticity. The evolution equation of a single dislocation is connected to the formation of kinks and jogs due to cutting by other dislocations and is shown to parallel the evolution equation of the dislocation density tensor in finite deformation formulation. Implications for dislocation based modeling of plasticity are discussed. Plastic deformation of crystals is mostly mediated by the motion of dislocations. During the last two decades a lot of effort was directed towards including more knowledge about dislocations in continuum descriptions of plasticity. Here the author derives the kinematics of single dislocations moving inside a dislocated crystal simultaneously deforming by the motion of other dislocations in the language of large deformation plasticity. The evolution equation of a single dislocation is connected to the formation of kinks and jogs due to cutting by other dislocations and is shown to parallel the evolution equation of the dislocation density tensor in finite deformation formulation. Implications for dislocation based modeling of plasticity are discussed. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Originalspracheenglisch
Seiten (von - bis)252-268
FachzeitschriftZeitschrift für angewandte Mathematik und Mechanik
Jahrgang93
Ausgabenummer4
DOIs
PublikationsstatusVeröffentlicht - 2013

Fingerprint

Dislocation
Plasticity
Dislocations (crystals)
Crystals
Tensors
Plastic deformation
Kinematics
Evolution Equation
Crystal
Continuum
Finite Deformation
Motion
Kink
Plastic Deformation
Large Deformation
Tensor
Formulation
Modeling

Schlagwörter

    ASJC Scopus subject areas

    • !!Mechanical Engineering

    Dies zitieren

    Moving dislocations in finite plasticity: a topological approach. / Hochrainer, Thomas.

    in: Zeitschrift für angewandte Mathematik und Mechanik, Jahrgang 93, Nr. 4, 2013, S. 252-268.

    Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

    @article{a561e4cea7f24a4fbb7f36d0a64dcf55,
    title = "Moving dislocations in finite plasticity: a topological approach",
    abstract = "Plastic deformation of crystals is mostly mediated by the motion of dislocations. During the last two decades a lot of effort was directed towards including more knowledge about dislocations in continuum descriptions of plasticity. Promising approaches towards building continuum plasticity theories on averages of the behavior of many single dislocations have been formulated under the assumption of small deformations. In the current paper we derive the kinematics of single dislocations moving inside a dislocated crystal simultaneously deforming by the motion of other dislocations in the language of large deformation plasticity. The evolution equation of a single dislocation is connected to the formation of kinks and jogs due to cutting by other dislocations and is shown to parallel the evolution equation of the dislocation density tensor in finite deformation formulation. Implications for dislocation based modeling of plasticity are discussed. Plastic deformation of crystals is mostly mediated by the motion of dislocations. During the last two decades a lot of effort was directed towards including more knowledge about dislocations in continuum descriptions of plasticity. Here the author derives the kinematics of single dislocations moving inside a dislocated crystal simultaneously deforming by the motion of other dislocations in the language of large deformation plasticity. The evolution equation of a single dislocation is connected to the formation of kinks and jogs due to cutting by other dislocations and is shown to parallel the evolution equation of the dislocation density tensor in finite deformation formulation. Implications for dislocation based modeling of plasticity are discussed. {\circledC} 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.",
    keywords = "Differential topology, Dislocations, Finite plasticity",
    author = "Thomas Hochrainer",
    year = "2013",
    doi = "10.1002/zamm.201100159",
    language = "English",
    volume = "93",
    pages = "252--268",
    journal = "Zeitschrift f{\"u}r angewandte Mathematik und Mechanik",
    issn = "0044-2267",
    publisher = "Wiley-VCH",
    number = "4",

    }

    TY - JOUR

    T1 - Moving dislocations in finite plasticity: a topological approach

    AU - Hochrainer, Thomas

    PY - 2013

    Y1 - 2013

    N2 - Plastic deformation of crystals is mostly mediated by the motion of dislocations. During the last two decades a lot of effort was directed towards including more knowledge about dislocations in continuum descriptions of plasticity. Promising approaches towards building continuum plasticity theories on averages of the behavior of many single dislocations have been formulated under the assumption of small deformations. In the current paper we derive the kinematics of single dislocations moving inside a dislocated crystal simultaneously deforming by the motion of other dislocations in the language of large deformation plasticity. The evolution equation of a single dislocation is connected to the formation of kinks and jogs due to cutting by other dislocations and is shown to parallel the evolution equation of the dislocation density tensor in finite deformation formulation. Implications for dislocation based modeling of plasticity are discussed. Plastic deformation of crystals is mostly mediated by the motion of dislocations. During the last two decades a lot of effort was directed towards including more knowledge about dislocations in continuum descriptions of plasticity. Here the author derives the kinematics of single dislocations moving inside a dislocated crystal simultaneously deforming by the motion of other dislocations in the language of large deformation plasticity. The evolution equation of a single dislocation is connected to the formation of kinks and jogs due to cutting by other dislocations and is shown to parallel the evolution equation of the dislocation density tensor in finite deformation formulation. Implications for dislocation based modeling of plasticity are discussed. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

    AB - Plastic deformation of crystals is mostly mediated by the motion of dislocations. During the last two decades a lot of effort was directed towards including more knowledge about dislocations in continuum descriptions of plasticity. Promising approaches towards building continuum plasticity theories on averages of the behavior of many single dislocations have been formulated under the assumption of small deformations. In the current paper we derive the kinematics of single dislocations moving inside a dislocated crystal simultaneously deforming by the motion of other dislocations in the language of large deformation plasticity. The evolution equation of a single dislocation is connected to the formation of kinks and jogs due to cutting by other dislocations and is shown to parallel the evolution equation of the dislocation density tensor in finite deformation formulation. Implications for dislocation based modeling of plasticity are discussed. Plastic deformation of crystals is mostly mediated by the motion of dislocations. During the last two decades a lot of effort was directed towards including more knowledge about dislocations in continuum descriptions of plasticity. Here the author derives the kinematics of single dislocations moving inside a dislocated crystal simultaneously deforming by the motion of other dislocations in the language of large deformation plasticity. The evolution equation of a single dislocation is connected to the formation of kinks and jogs due to cutting by other dislocations and is shown to parallel the evolution equation of the dislocation density tensor in finite deformation formulation. Implications for dislocation based modeling of plasticity are discussed. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

    KW - Differential topology

    KW - Dislocations

    KW - Finite plasticity

    U2 - 10.1002/zamm.201100159

    DO - 10.1002/zamm.201100159

    M3 - Article

    VL - 93

    SP - 252

    EP - 268

    JO - Zeitschrift für angewandte Mathematik und Mechanik

    JF - Zeitschrift für angewandte Mathematik und Mechanik

    SN - 0044-2267

    IS - 4

    ER -