2015/09/03 by Giovanni A. Bonaschi, Bonaschi, Giovanni A., Patrick Meurs +4
Engineering · Materials Science · Mathematics · Physics and Astronomy · #34A60 #49J40 #70F99 #74Bxx #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #Elasticity and Material Modeling #FOS: Mathematics #Model Reduction and Neural Networks #Nonlocal and gradient elasticity in micro/nano structures #math.CA #math.DS #msc:34A60 #msc:49J40 #msc:70F99 #msc:74Bxx
paper · pdf · doi:10.48550/arxiv.1509.01019
17 pages, 2 figures http://cvgmt.sns.it/paper/2781/
openalex publication_date 2015/09/03 · arxiv created 2016/02/29 · arxiv updated 2016/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 generalisation of the setting in [AGS08, Chap. 2 and 3] that allows for dissipations which cannot be described by a metric.