Blog
About

4
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      An existence result for Discrete Dislocation Dynamics in three dimensions

      Preprint

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          We present a mathematical framework within which Discrete Dislocation Dynamics in three dimensions is well-posed. By considering smooth distributions of slip, we derive a regularised energy for curved dislocations, and rigorously derive the Peach-Koehler force on the dislocation network via an inner variation. We propose a dissipative evolution law which is cast as a generalised gradient flow, and using a discrete-in-time approximation scheme, existence and regularity results are obtained for the evolution, up until the first time at which an infinite density of dislocation lines forms.

          Related collections

          Most cited references 44

          • Record: found
          • Abstract: not found
          • Article: not found

          The size of a dislocation

           R. Peierls (1940)
            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            The Mechanism of Plastic Deformation of Crystals. Part I. Theoretical

             G I Taylor (1934)
              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              The Forces Exerted on Dislocations and the Stress Fields Produced by Them

               M Peach,  J. Koehler (1950)
                Bookmark

                Author and article information

                Journal
                01 June 2018
                Article
                1806.00304

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                35Q74, 74N05, 37N15
                30 pages, 3 figures
                math.AP

                Analysis

                Comments

                Comment on this article