Gamma-convergence analysis for finite systems of dislocations.

Datum

19.06.2014

Zeit

15:30 - 16:30

Sprecher

Dr. Lucia De Luca

Zugehörigkeit

TU Dresden, Institut für Analysis

Serie

TUD Mathematik Oberseminar Analysis

Sprache

en

Hauptthema

Mathematik

Andere Themen

Mathematik

Host

Prof. Dr. R. Chill

Beschreibung

Dislocations are line defects in the periodic structure of the crystals and they play a prominent role in the plastic deformations of metals. We will focus on the case of straight dislocations, which are usually classified in two main types: screw and edge. We will consider the elastic energy induced by finite systems of screw (resp. edge) dislocations in the framework of linearized antiplanar (resp. plane) elasticity. In this context, dislocations can be defined as point topological defects of the displacement gradient field. Introducing a parameter $varepsilon>0$, which represents the lattice spacing of the crystal, we will analyze in terms of Gamma-convergence the asymptotic behavior of the elastic energy stored in the crystal as $varepsilon o 0$. We will see that this analysis exhibits many similarities with the one given for the vortices in superconductors in the Ginzburg-Landau framework. Finally, we will show that in the scalar case of screw dislocations, we can obtain the energy Gamma-expansion, which is not yet available in the vectorial case of edge dislocations. The results are obtained in collaboration with Roberto Alicandro, Adriana Garroni and Marcello Ponsiglione.

Links

• Webseite zum Oberseminar Analysis

Letztmalig verändert: 30.04.2014, 13:00:37