On the material geometry of continuously defective corrugated graphene sheets
arXiv:1407.1396
Abstract
Geometrical objects describing the material geometry of continuously defective graphene sheets are introduced and their compatibility conditions are formulated. Effective edge dislocations embedded in the Riemann-Cartan material space and defined by their scalar density and by local Burgers vectors, are considered. The case of secondary curvature-type defects created by this distribution of dislocations is analysed in terms of the material space. The variational geometry of the material space closely related with the existence of a characteristic length parameter is proposed. The formula which describes, in a reference temperature, the influence of dislocations on the material Riemannian metric, is given.
38 pages. Keywords: non-Euclidean geometry, orthogonal space, variational geometry, Riemann-Cartan space, surface, Gauss curvature, vectorial torsion, material geometry, isothermal geometry, material space, configurational space, embedding, curvature-type defect, line defect, dislocation, disclination, Burgers vector, Frank vector, graphene, graphene sheet, corrugation