Calculus of Variations and Geometric Measure Theory

A. Garroni - R. Marziani - R. Scala

Derivation of a line-tension model for dislocations from a nonlinear three-dimensional energy: the case of the quadratic growth

created by scala on 04 Apr 2020
modified by garroni1 on 24 Mar 2022


Published Paper

Inserted: 4 apr 2020
Last Updated: 24 mar 2022

Journal: SIAM J. Math. Anal.
Volume: 53
Number: 4
Pages: 4252-4302
Year: 2021

ArXiv: 2004.01983 PDF


In this paper we derive a line tension model for dislocations in 3d starting from a geometrically nonlinear elastic energy with quadratic growth. In the asymptotic analysis, as the amplitude of the Burgers vectors (proportional to the lattice spacing) tends to zero, we show that the elastic energy linearises and the line tension energy density, up to an overall constant rotation, is identified by the linearised cell problem formula given in 17.