Location
MC 6460
Speaker
Marco Morandotti, Department of Mathematical Sciences, Politecnico di Torino
Title
Variational modeling of disclinations
Abstract
Disclinations in crystalline materials are point defects that are responsible for rotational kinematic incompatibility. They are characterised by the so-called Frank angle, measuring the severity of the lattice mismatch. In a two-dimensional medium under the assumption of plain strain, the Airy stress function can be used to translate the measure of incompatibility into a fourth-order PDE with measure data.
We propose a variational model for disclinations in two-dimensional materials by means of the core-radius approach. Moreover, we identify a good scaling regime in which we study the effective behaviour of dipoles of disclinations (of opposite signs), thus validating analytically the results obtained in [Eshelby, 1966]: a dipole of plane disclinations generates an edge dislocation with Burgers vector perpendicular to the dipole axis. Finally, we study the energy of a system of a finite number of dipoles of disclinations and recover the results of [Cermelli-Leoni, 2005] for edge dislocations.
This is work in collaboration with Pierluigi Cesana (Kyushu University) and Lucia De Luca (CNR Rome).