Upscaling of the dynamics of dislocation walls

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

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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 [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.
Original languageEnglish
Pages (from-to)401-414
JournalAdvances in Mathematical Sciences and Applications
Volume24
Issue number2
Publication statusPublished - 2014

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Meurs, van, P. J. P., & Muntean, A. (2014). Upscaling of the dynamics of dislocation walls. Advances in Mathematical Sciences and Applications, 24(2), 401-414.