Semi-Discrete Modeling of Systems of Disclinations and Dislocations in Crystalline Materials

Explore a comprehensive lecture on semi-discrete modeling of systems of disclinations and dislocations in crystalline materials. Delve into the concept of disclinations as point defects responsible for rotational kinematic incompatibility, characterized by the Frank angle. Learn how the Airy stress function translates incompatibility measures into a fourth-order PDE with measure data in two-dimensional media under plain strain. Examine a proposed variational model for disclinations using the core-radius approach and investigate the effective behavior of disclination dipoles. Discover how this analysis validates Eshelby's 1966 findings on edge dislocation generation. Study the energy of finite dipole systems and understand how it relates to Cermelli and Leoni's 2005 results for edge dislocations. Gain insights into topics such as incompatibility conditions, variational calculus, elastic energy, and solution methods throughout this 36-minute talk, which was part of the "Between Regularity and Defects: Variational and Geometrical Methods in Materials Science" workshop held at the Erwin Schrödinger International Institute for Mathematics and Physics.

Introduction
Overview
Dislocations
Energy minimization
Incompatibility conditions
Variational calculus
Elastic energy
Solution
Results