Presentation on

“The stress-strain behavior of polymer-nanotube composites from molecular dynamics simulation”S.J.V. Frankland , V.M.Harik , G.M.Odegard , D.W. Brenner , T.S.Gates

Presented By-Saeedur Rahman- 0910001Saddam Hossain joy- 0910051Jahidul Islam Rakib- 0910059

Presented To-Dr. Monon MahboobAssistant Professor,Department of Mechanical Engineering, BUET

Objectives…..

• To investigate the stress-strain behavior of polyethylene-carbon nanotube composite mechanically loaded in both the longitudinal and transverse direction

• To compare the response of the composite to mechanical loading with a long , continuous nanotube and with a short , discontinuous nanotube

RVE….

Mechanical loading……

Numerical method…• Molecular dynamics simulation is

used• MD simulation package used- DL-

POLY -Daresbury Laboratory• The overall dimensions for the

unit cell in the MD simulation is 5×5×10 nm

• The density of the polyethylene used is

.71 g/cm³• Time step used 2 fs• All simulation is carried out at 300

k

Boundary condition – • Periodic boundary condition is

used to replicate the cell in all three dimension

Numerical method…

• MD simulation actually generates the atomic trajectories of a system of N particles by numerical integration of Newton’s equation of motion

• The van der Waals Interaction between polymer and NT is modeled with Lennard-Jones potential

• Bond length is modeled by using SHAKE algorithm

Numerical method…• Angle bending force is modeled by

Harmonic valence angle potential• A torsional potential is also used of

the form-

Strain-• Applied strain increment - 2% is applied in two equal increments of 1% each 1ps (500 step) apart• after each 2% increment of strain,

the system was relaxed for 2 ps and then the stress on the system was averaged over an interval of 10 ps

• six increments of 2% strain were applied up to a total of approximately 12% over a period of 72 ps

Numerical method… Stress • defined as the change in the internal energy

with respect to the strain per unit volume-

• At the atomic level, the total internal energy for each atom is

• So stress contribution for a atom-

• So average atomic stresses for the volume of the model-

Rule of mixture….• The longitudinal elastic modulus of

the composite cell with long NTs under constant-strain conditions is-

• For transverse loading –

• Volume fraction of carbon nanotube can be determined as-

Results and Discussion…

Results and Discussion…

THANK YOU….