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      An existence result for Discrete Dislocation Dynamics in three dimensions

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          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.

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          Most cited references42

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

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            Normal and Integral Currents

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              Mathematical theory of stationary dislocations

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                Author and article information

                Journal
                01 June 2018
                Article
                1806.00304
                8281960d-66df-4532-9adb-3225a4107fa2

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

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

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