Semi-discrete modeling of systems of disclinations and dislocations

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).

MathematicsPhysics

Audience: researchers in the topic

---

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)

---