【Seminar】Semi-discrete modeling of systems of disclinations and dislocations by Prof. Marco Morandotti
Dr. Marco Morandotti, Associate Professor, Department of Mathematical Sciences of Politecnico di Torino.
Marco Morandotti was awarded a PhD in Applied Mathematics from SISSA (Trieste, Italy) and since then he has been an associate researcher at Carnegie Mellon University (Pittsburgh, USA), Instituto Superior Técnico (Lisbon, Portugal), SISSA (Trieste, Italy), and Technische Universität München (Munich, Germany), before joining Politecnico di Torino, where he is now an associate professor at the Department of Mathematical Sciences.
His research interests are in mathematical analysis with application to sciences, including the calculus of variations, the mechanics of materials, the dynamics of multi-agent systems.
Disclinations in crystalline materials are point defects that are responsible for rotational kinematic incompatibility. They are characterized 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 behavior 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).
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