Forces on dislocations and the limits of classical elasticity in 2D

Abstract

This thesis investigates some limits of the classical theory of elasticity in 2D, especially concerning forces on topological defects called dislocations. Initially, the thesis comments each approximating step used in deriving Classical Elasticity. Novel discussions are made about the continuum assumption and the limits of the sum-to- integral approximation. Moreover, an alternative mathematical formalism to deformations in 2D is introduced in order to obtain simpler equations and physical inferences. Thereafter, the notion of the core force is studied. This is a correction to the classical force on dislocation, called Peach-Koehler force, and which appears when in the presence of strain gradients. It has been predicted by different approaches but never observed, until a work which is presented in this thesis. A simulation model to investigate such force and its results are shown. By comparing with the previous theoretical approaches, it is verified that none of them is capable of providing a way to quantitatively predict the core force. Furthermore, it is shown that, for some systems, results from the core force can be used to predict a definite value for the core energy of the dislocation.