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“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-