Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity
Analysis of PDEs
2016-11-14 v1
Abstract
In the modeling of dislocations one is lead naturally to energies concentrated on lines, where the integrand depends on the orientation and on the Burgers vector of the dislocation, which belongs to a discrete lattice. The dislocations may be identified with divergence-free matrix-valued measures supported on curves or with 1-currents with multiplicity in a lattice. In this paper we develop the theory of relaxation for these energies and provide one physically motivated example in which the relaxation for some Burgers vectors is nontrivial and can be determined explicitly. From a technical viewpoint the key ingredients are an approximation and a structure theorem for 1-currents with multiplicity in a lattice.
Keywords
Cite
@article{arxiv.1409.6084,
title = {Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity},
author = {Sergio Conti and Adriana Garroni and Annalisa Massaccesi},
journal= {arXiv preprint arXiv:1409.6084},
year = {2016}
}