Energies Concentrated on Lines and the Modeling of Dislocations in 3D

Thursday, May 22, 2014 - 3:50pm - 4:30pm
Keller 3-180
Adriana Garroni (Università di Roma La Sapienza)
Dislocations are topological singularities in crystals, which may be described
by lines to which a lattice-valued vector, called Burgers vector, is associated.
They may be identified with divergence-free matrix-valued measures
supported on curves or with 1-currents with multiplicity in a lattice.
In the modeling of dislocations one is thus often lead to energies concentrated
on lines, where the integrand depends on the orientation and on the Burgers
vector of the dislocation.
In this talk I will present the theory of relaxation for such energies and
I will show how they may arise in a multiscale analysis of dislocations,
starting from discrete and semi-discrete models.
MSC Code: