Dislocation Field Theory in 2D: Application to Graphene

TL;DR

This paper introduces a 2D dislocation continuum theory for graphene, incorporating elastic rotation, dislocation density, and background stress, with solutions that align well with experimental data.

Contribution

It develops a novel 2D dislocation theory with four material moduli and characteristic length scales, extending classical elasticity for graphene applications.

Findings

Non-singular stress and distortion solutions for edge dislocations

Good agreement with experimental strain data in graphene

Introduction of two characteristic length scales in the theory

Abstract

A two-dimensional (2D) dislocation continuum theory is being introduced. The present theory adds elastic rotation, dislocation density, and background stress to the classical energy density of elasticity. This theory contains four material moduli. Two characteristic length scales are defined in terms of the four material moduli. Non-singular solutions of the stresses and elastic distortions of an edge dislocation are calculated. It has been pointed out that the elastic strain agrees well with experimental data found recently for an edge dislocation in graphene.