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Computational Study of Carbon Nanotubes under Compressive Loading PowerPoint Presentation

Computational Study of Carbon Nanotubes under Compressive Loading

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Computational Study of Carbon Nanotubes under Compressive Loading

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Computational Study of Carbon Nanotubes under Compressive Loading

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- Computational Study of Carbon Nanotubes under Compressive Loading
- Quasi-static reduced-order general continuum method with
- barycentric Interpolation

Yang Yang, William W. Liou

Computational Engineering Physics Lab

Western Michigan University

Kalamazoo, Michigan

36th Dayton-Cincinnati Aerospace Sciences Symposium

03/01/2011

Introduction

Properties of carbon nanotubes

Applications of carbon nanotubes

Definition of carbon nanotubes

Numerical method

Overview

Reduced-order general continuum method

Simulation results

Model setup

Buckling patterns

Buckling patterns after barycentric conversion

Loading-unloading stress-strain curves for CNTs of

different types

Conclusions

Introduction

Properties of carbon nanotubes

Applications of carbon nanotubes

Definition of carbon nanotubes

Numerical method

Overview

Reduced-order general continuum method

Simulation results

Model setup

Buckling patterns

Buckling patterns after barycentric conversion

Loading-unloading stress-strain curves for CNTs of

different types

Conclusions

Introduction

Properties of carbon nanotubes

- Average diameter of SWNT

- Carbon bond length

- Density

- Thermal conductivity

- Young’s modulus of SWNT

- Max. tensile strength

Introduction

Properties of carbon nanotubes

- Composed of all-carbon molecules in shell-like cylindrical
- structure formed by strong covalent bonding of atoms

- Tend to undergo buckling with compression or bending loads

- One of the strongest materials known, both in terms of tensile
- strength and elastic modulus

Introduction

Applications of carbon nanotubes

- Carbon nanotubes enhanced composite materials

- Efficient heat remover composed of aligned structures and ribbons of CNTs

- Drug delivery to prevent medicine from damaging healthy cells

- Intrinsic tubule character of CNTs attributing to their very high surface area leads to the applications in energy storage material

- Used as electrical conducting additives to producing conductive plastics

- Flat panel CNT field emission display

Introduction

Definition of carbon nanotubes

Introduction

Properties of carbon nanotubes

Applications of carbon nanotubes

Definition of carbon nanotubes

Numerical method

Overview

Reduced-order general continuum method

Simulation results

Model setup

Buckling patterns

Buckling patterns after barycentric conversion

Loading-unloading stress-strain curves for CNTs of

different types

Conclusions

Numerical method

Overview

- Classical molecular dynamics (MD)

Excels in modeling structural details of an atomic system by tracking

each atom

Computationally prohibitive for large systems; generally modeling a

system with the size up to a few hundred nanometers

- Reduced-order general continuum method

Constitutive law is built based on an atomistic energy function by

intrinsic geometric quantities describing a deformation

No need for tracking individual atoms thus appropriate for modeling a

large system

Reduced-order general continuum method

- General idea

Every point in the continuum body

is described by a representative atom

embedded in a crystallite of radius

Finite elements discretizing the

continuum body

Reduced-order general continuum method

- Cauchy-Born rule

- Exponential map

Reduced-order general continuum method

- REBO potential function for CNT

The repulsive pair:

The attractive pair:

The bond order term:

Reduced-order general continuum method

- Lennard-Jones potential for long-range interaction

Reduced-order general continuum method

- Atomic potential energies expressed in continuum variables

Interatomic energy density

Total interatomic energy over the CNT surface

Long-range Lennard-Jones energy for the CNT

- Total energy of the CNT

- Equilibrium state of the CNT correspondsMin ( )

Introduction

Properties of carbon nanotubes

Applications of carbon nanotubes

Definition of carbon nanotubes

Numerical method

Overview

Reduced-order general continuum method

Simulation results

Model setup

Buckling patterns

Buckling patterns after barycentric conversion

Loading-unloading stress-strain curves for CNTs of

different types

Conclusions

Model setup

Fixed

end

Displacement

control B.C.

- Buckling of different types of CNT under compressive loading

CNT cases studied

- Displacement control method is used to apply the loading

Buckling patterns

- Van der Waals energy vs. strain Case 1

- Total energy vs. strain Case 1

buckling

Buckling patterns

Case 1

Case 2

Case 3

Case 4

before

after

Buckling patterns

Buckling patterns after barycentric conversion

- Buckled state for Case 1

- Incipient state for Case 1

- Buckling events for Case 1

Buckling patterns after barycentric conversion

- Representative cells on the buckling surface of CNTs with different chiral angles.

(14, 0) CNT Case 1

(8, 8) CNT Case 4

(12, 3) CNT Case 2

(10, 5) CNT Case 3

- The number of bonds that receives compressive load increases from Case 1 to Case 4

- The bonds are compressed more uniformly in Case 4 than in Case 2 or Case 3

Introduction

Properties of carbon nanotubes

Applications of carbon nanotubes

Definition of carbon nanotubes

Numerical method

Overview

Reduced-order general continuum method

Simulation results

Model setup

Buckling patterns

Buckling patterns after barycentric conversion

Loading-unloading stress-strain curves for CNTs of

different types

Conclusions

- The reduced order general continuum method was used to study the behaviors of CNTs under compressive loading conditions.
- Reverse mapping of the finite element results to the associated CNT lattice deformation using barycentric interpolation.
- Different buckled configurations will be assumed by CNTs with different chiral angles.
- The zigzag CNT has the most apparent buckling pattern.
- The buckling strain increases with the increasing chiral angle.
- The armchair CNT has the strongest resistance to the compressive loading.