Dislocation Field Theory in 2D: Application to Graphene

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.

References in corpus (6)

• Topological Defects in Graphene: Dislocations and Grain Boundaries
• Finite temperature lattice properties of graphene beyond the quasiharmonic approximation
• The gauge theory of dislocations: static solutions of screw and edge dislocations
• The gauge theory of dislocations: conservation and balance laws
• On the Higgs mechanism and stress functions in the translational gauge theory of dislocations
• Strain and rotation fields of dislocations in graphene

Cited by in corpus (3)

• Novel effects of strains in graphene and other two dimensional materials
• Micromechanics of dislocations in solids: $J$-, $M$-, and $L$-integrals and their fundamental relations
• Elastic Liénard-Wiechert potentials of dynamical dislocations from tensor gauge theory in 2+1 dimensions