Calculus of Variations and Geometric Measure Theory

I. Lucardesi - M. Morandotti - R. Scala - D. Zucco

Upscaling of screw dislocations with increasing tangential strain

created by morandott on 27 Aug 2018
modified on 19 May 2020


Published Paper

Inserted: 27 aug 2018
Last Updated: 19 may 2020

Journal: Rend. Lincei Mat. Appl.
Volume: 31
Pages: 419-443
Year: 2020

ArXiv: 1808.08898 PDF


The upscaling of a system of screw dislocations in a material subject to an external strain is studied. The $\Gamma$-limit of a suitable rescaling of the renormalized energy is characterized in the space of probability measures. This corresponds to a discrete-to-continuum limit of the dislocations, which, as a byproduct, provides information on their distribution when the circulation of the tangential component of the external strain becomes larger and larger. In particular, dislocations are shown to concentrate at the boundary of the material and to distribute as the limiting external strain.

Keywords: $\Gamma$-convergence, dislocations, core radius approach, divergence-measure fields, discrete-to-continuum limit, Ginzburg-Landau vortices