Modeling continuous distributions of dislocations in multi-walled nanotube composites

A modeling paradigm for continuous distributions of defects in multi-walled nanotube composites is proposed based on the theory of differential forms. A necessary and sufficient condition for a defect-free composite is derived and, concomitantly, a measure of defect density is proposed. Mathematical...

Full description

Saved in:
Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2016-12, Vol.67 (6), p.1-16, Article 141
Main Author: Epstein, Marcelo
Format: Article
Language:English
Subjects:
Applications of mathematics
Coherence
Composite materials
Consistency
Defects
Density
Dislocations
Engineering
Mathematical Methods in Physics
Modelling
Nanostructure
Nanotubes
Partial differential equations
Theoretical and Applied Mechanics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A modeling paradigm for continuous distributions of defects in multi-walled nanotube composites is proposed based on the theory of differential forms. A necessary and sufficient condition for a defect-free composite is derived and, concomitantly, a measure of defect density is proposed. Mathematically, this condition ensures the consistency of an overdetermined system of partial differential equations. Physically, the condition expresses the fact that each multilayered nanotube can find mutually coherent nanotubes in its neighborhood. Several examples of defect-free arrangements are presented and discussed.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-016-0737-9