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 language | English |
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Pages (from-to) | 401-414 |
Journal | Advances in Mathematical Sciences and Applications |
Volume | 24 |
Issue number | 2 |
Publication status | Published - 2014 |