Upscaling of the dynamics of dislocation walls

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

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

Samenvatting

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 [14]. 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 G-convergence of the respective energies are properties of paramount importance for our arguments. Keywords: Discrete-to-continuum limit, Gamma-convergence, gradiet flows, dislocations.
Originele taal-2Engels
Pagina's (van-tot)401-414
TijdschriftAdvances in Mathematical Sciences and Applications
Volume24
Nummer van het tijdschrift2
StatusGepubliceerd - 2014

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