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 . 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.
|Journal||Advances in Mathematical Sciences and Applications|
|Publication status||Published - 2014|