TY - RPRT
T1 - Dynamics of screw dislocations: a generalised minimising-movements scheme approach
Y1 - 2015
A1 - Giovanni A. Bonaschi
A1 - Patrick Van Meurs
A1 - Marco Morandotti
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.
PB - SISSA
UR - http://urania.sissa.it/xmlui/handle/1963/34495
U1 - 34692
U2 - Mathematics
U4 - 1
ER -