Upscaling of the dynamics of dislocation walls

P.J.P. Meurs, van, A. Muntean

Research output: Book/ReportReportAcademic

40 Downloads (Pure)

Abstract

We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of the upscaling procedure (i.e. the discrete-to-continuum passage) relies on the gradient flow structure of both the discrete and continuous energies of dislocations set in a suitable evolutionary variational inequality framework. Moreover, the convexity and I'-convergence of the respective energies are properties of paramount importance for our arguments.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages11
Publication statusPublished - 2014

Publication series

NameCASA-report
Volume1432
ISSN (Print)0926-4507

Fingerprint

continuums
convexity
gradients
energy

Cite this

Meurs, van, P. J. P., & Muntean, A. (2014). Upscaling of the dynamics of dislocation walls. (CASA-report; Vol. 1432). Eindhoven: Technische Universiteit Eindhoven.
Meurs, van, P.J.P. ; Muntean, A. / Upscaling of the dynamics of dislocation walls. Eindhoven : Technische Universiteit Eindhoven, 2014. 11 p. (CASA-report).
@book{bab4b67f12d342c4a225357891177a17,
title = "Upscaling of the dynamics of dislocation walls",
abstract = "We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of the upscaling procedure (i.e. the discrete-to-continuum passage) relies on the gradient flow structure of both the discrete and continuous energies of dislocations set in a suitable evolutionary variational inequality framework. Moreover, the convexity and I'-convergence of the respective energies are properties of paramount importance for our arguments.",
author = "{Meurs, van}, P.J.P. and A. Muntean",
year = "2014",
language = "English",
series = "CASA-report",
publisher = "Technische Universiteit Eindhoven",

}

Meurs, van, PJP & Muntean, A 2014, Upscaling of the dynamics of dislocation walls. CASA-report, vol. 1432, Technische Universiteit Eindhoven, Eindhoven.

Upscaling of the dynamics of dislocation walls. / Meurs, van, P.J.P.; Muntean, A.

Eindhoven : Technische Universiteit Eindhoven, 2014. 11 p. (CASA-report; Vol. 1432).

Research output: Book/ReportReportAcademic

TY - BOOK

T1 - Upscaling of the dynamics of dislocation walls

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

AU - Muntean, A.

PY - 2014

Y1 - 2014

N2 - We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of the upscaling procedure (i.e. the discrete-to-continuum passage) relies on the gradient flow structure of both the discrete and continuous energies of dislocations set in a suitable evolutionary variational inequality framework. Moreover, the convexity and I'-convergence of the respective energies are properties of paramount importance for our arguments.

AB - We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of the upscaling procedure (i.e. the discrete-to-continuum passage) relies on the gradient flow structure of both the discrete and continuous energies of dislocations set in a suitable evolutionary variational inequality framework. Moreover, the convexity and I'-convergence of the respective energies are properties of paramount importance for our arguments.

M3 - Report

T3 - CASA-report

BT - Upscaling of the dynamics of dislocation walls

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -

Meurs, van PJP, Muntean A. Upscaling of the dynamics of dislocation walls. Eindhoven: Technische Universiteit Eindhoven, 2014. 11 p. (CASA-report).