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

Show simple item record Bonaschi, Giovanni A. Van Meurs, Patrick Morandotti, Marco 2015-09-04T08:57:37Z 2015-09-04T08:57:37Z 2015
dc.description.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. en_US
dc.language.iso en en_US
dc.publisher SISSA en_US
dc.relation.ispartofseries SISSA;38/2015/MATE
dc.subject Motion of dislocations en_US
dc.subject Generalised gradient flows en_US
dc.subject minimising-movement scheme en_US
dc.subject energy dissipation inequality en_US
dc.title Dynamics of screw dislocations: a generalised minimising-movements scheme approach en_US
dc.type Preprint en_US
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US

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