TY - BOOK

T1 - Dynamics of screw dislocations : a generalised minimising-movements scheme approach

AU - Bonaschi, G.A.

AU - Meurs, van, P.J.P.

AU - Morandotti, M.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

M3 - Report

T3 - CASA-report

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

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -