Dynamics of screw dislocations : a generalised minimising-movements scheme approach

G.A. Bonaschi, P.J.P. Meurs, van, M. Morandotti

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Abstract

The gradient flow structure of the model introduced in [CG99] for the dynamics of screw dislocations is investigated by means of a generalised minimising-movements scheme approach. The assumption of a finite number of available glide directions, together with the "maximal dissipation criterion" that governs the equations of motion, results into solving a differential inclusion rather than an ODE. This paper addresses how the model in [CG99] is connected to a time-discrete evolution scheme which explicitly confines dislocations to move each time step along a single glide direction. It is proved that the time-continuous model in [CG99] is the limit of these time-discrete minimising-movement schemes when the time step converges to 0. The study presented here is a first step towards a generalization of the setting in [AGS08, Chap. 2 and 3] that allows for dissipations which cannot be described by a metric. Keywords: Motion of dislocations, generalised gradient flows, minimising-movement scheme, energy dissipation inequality.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages16
Publication statusPublished - 2015

Publication series

NameCASA-report
Volume1531
ISSN (Print)0926-4507

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