Moving dislocations in finite plasticity: a topological approach


  • T. Hochrainer

    1. Institut für Zuverlässigkeit von Bauteilen und Systemen, Kaiserstr. 12, Karlsruher Institut für Technologie KIT, 76131 Karlsruhe, Germany
    2. Current address: BIME – Bremer Institut für Strukturmechanik und Produktionsanlagen, Universität Bremen, IW3, Am Biologischen Garten 2, 28359 Bremen, Germany
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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.