1. by Wing Kam Liu, Eduard G. Karpov, Harold S. Park
Nano Mechanics and Materials: Theory, Multiscale Methods and Applications by
Wing Kam Liu, Eduard G. Karpov, Harold S. Park

2. 8. Non-Nearest Neighbor MD Boundary Condition

3. Motivation to Non-Nearest Neighbor Interaction Modeling
Atomic interactions inherently non-local
Some potentials have angular dependence
Usage of nearest neighbor potentials leads to different physics being displayed (Holian, Physical Review A 1991), particularly at large deformations/high strain rates
Need to account for non-nearest neighbor interactions in impedance force
Impedance Force

4. Pairwise vs. Many-body Potential
Morse pair potential
EAM many-body potential
Both images taken from Holian et al., Physical Review A 1991; 43:

5. MD Impedance Boundary Condition
There are 4 ’s for second-nearest neighbor interactions instead of 1 for nearest neighbor interactions 1 2 3
Eliminated Atoms
Boundary atoms

6. Numerical Examples – 1D Wave Propagation
Problem Description:
Non-nearest neighbor harmonic potential of form:
Initial MD displacements like
previous 1D examples
10 atoms per finite element
MD energy transfer if MD impedance force applied correctly

7. 1D MD Wave Propagation
Problem Description:
Harmonic potential of form:
Gaussian wave initial
displacements
Second neighbor interactions
Initial MD displacements

8. 1D MD Wave Propagation
MD region energy transfer