Dynamics of screw dislocations: a generalised minimising-movements scheme approach
| dc.contributor.area | Mathematics | en_US |
| dc.contributor.author | Bonaschi, Giovanni A. | |
| dc.contributor.author | Van Meurs, Patrick | |
| dc.contributor.author | Morandotti, Marco | |
| dc.date.accessioned | 2015-09-04T08:57:37Z | |
| dc.date.available | 2015-09-04T08:57:37Z | |
| dc.date.issued | 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.identifier.uri | https://openscience.sissa.it/handle/1963/34495 | |
| dc.language.iso | en | en_US |
| dc.miur.area | 1 | 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 |