An existence result for Discrete Dislocation Dynamics in three dimensions

Thomas Hudson

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arXiv · 1806.00304

An existence result for Discrete Dislocation Dynamics in three dimensions

Thomas Hudson

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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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Thomas Hudson. 2018-06-01. An existence result for Discrete Dislocation Dynamics in three dimensions. https://arxiv.org/abs/1806.00304

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